[A prognostic model of a cholera epidemic].
Boev, B V; Bondarenko, V M; Prokop'eva, N V; San Román, R T; Raygoza-Anaya, M; García de Alba, R
1994-01-01
A new model for the prognostication of cholera epidemic on the territory of a large city is proposed. This model reflects the characteristic feature of contacting infection by sensitive individuals due to the preservation of Vibrio cholerae in their water habitat. The mathematical model of the epidemic quantitatively reflects the processes of the spread of infection by kinetic equations describing the interaction of the streams of infected persons, the causative agents and susceptible persons. The functions and parameters of the model are linked with the distribution of individuals according to the duration of the incubation period and infectious process, as well as the period of asymptomatic carrier state. The computer realization of the model by means of IBM PC/AT made it possible to study the cholera epidemic which took place in Mexico in 1833. The verified model of the cholera epidemic was used for the prognostication of the possible spread of this infection in Guadalajara, taking into account changes in the epidemiological situation and the size of the population, as well as improvements in sanitary and hygienic conditions, in the city.
Modeling Epidemic Network Failures
DEFF Research Database (Denmark)
Ruepp, Sarah Renée; Fagertun, Anna Manolova
2013-01-01
This paper presents the implementation of a failure propagation model for transport networks when multiple failures occur resulting in an epidemic. We model the Susceptible Infected Disabled (SID) epidemic model and validate it by comparing it to analytical solutions. Furthermore, we evaluate...... the SID model’s behavior and impact on the network performance, as well as the severity of the infection spreading. The simulations are carried out in OPNET Modeler. The model provides an important input to epidemic connection recovery mechanisms, and can due to its flexibility and versatility be used...... to evaluate multiple epidemic scenarios in various network types....
A social contagious model of the obesity epidemic
Huang, He; Yan, Zhijun; Chen, Yahong; Liu, Fangyan
2016-11-01
Obesity has been recognized as a global epidemic by WHO, followed by many empirical evidences to prove its infectiousness. However, the inter-person spreading dynamics of obesity are seldom studied. A distinguishing feature of the obesity epidemic is that it is driven by a social contagion process which cannot be perfectly described by the infectious disease models. In this paper, we propose a novel belief decision model based on the famous Dempster-Shafer theory of evidence to model obesity epidemic as the competing spread of two obesity-related behaviors: physical inactivity and physical activity. The transition of health states is described by an SIS model. Results reveal the existence of obesity epidemic threshold, above which obesity is quickly eradicated. When increasing the fading level of information spread, enlarging the clustering of initial obese seeds, or introducing small-world characteristics into the network topology, the threshold is easily met. Social discrimination against the obese people plays completely different roles in two cases: on one hand, when obesity cannot be eradicated, social discrimination can reduce the number of obese people; on the other hand, when obesity is eradicable, social discrimination may instead cause it breaking out.
Danon, Leon; Brooks-Pollock, Ellen
2016-09-01
In their review, Chowell et al. consider the ability of mathematical models to predict early epidemic growth [1]. In particular, they question the central prediction of classical differential equation models that the number of cases grows exponentially during the early stages of an epidemic. Using examples including HIV and Ebola, they argue that classical models fail to capture key qualitative features of early growth and describe a selection of models that do capture non-exponential epidemic growth. An implication of this failure is that predictions may be inaccurate and unusable, highlighting the need for care when embarking upon modelling using classical methodology. There remains a lack of understanding of the mechanisms driving many observed epidemic patterns; we argue that data science should form a fundamental component of epidemic modelling, providing a rigorous methodology for data-driven approaches, rather than trying to enforce established frameworks. The need for refinement of classical models provides a strong argument for the use of data science, to identify qualitative characteristics and pinpoint the mechanisms responsible for the observed epidemic patterns.
Cyber Epidemic Models with Dependences
Xu, Maochao; Da, Gaofeng; Xu, Shouhuai
2016-01-01
Studying models of cyber epidemics over arbitrary complex networks can deepen our understanding of cyber security from a whole-system perspective. In this paper, we initiate the investigation of cyber epidemic models that accommodate the {\\em dependences} between the cyber attack events. Due to the notorious difficulty in dealing with such dependences, essentially all existing cyber epidemic models have assumed them away. Specifically, we introduce the idea of Copulas into cyber epidemic mode...
Epidemic Survivability: Characterizing Networks Under Epidemic-like Failure Propagation Scenarios
DEFF Research Database (Denmark)
Manzano, Marc; Calle, Eusebi; Ripoll, Jordi
2013-01-01
Epidemics theory has been used in different contexts in order to describe the propagation of diseases, human interactions or natural phenomena. In computer science, virus spreading has been also characterized using epidemic models. Although in the past the use of epidemic models...... in telecommunication networks has not been extensively considered, nowadays, with the increasing computation capacity and complexity of operating systems of modern network devices (routers, switches, etc.), the study of possible epidemic-like failure scenarios must be taken into account. When epidemics occur......, such as in other multiple failure scenarios, identifying the level of vulnerability offered by a network is one of the main challenges. In this paper, we present epidemic survivability, a new network measure that describes the vulnerability of each node of a network under a specific epidemic intensity. Moreover...
An epidemic model for the future progression of the current Haiti cholera epidemic
Bertuzzo, E.; Mari, L.; Righetto, L.; Casagrandi, R.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.
2012-04-01
As a major cholera epidemic progresses in Haiti, and the figures of the infection, up to December 2011, climb to 522,000 cases and 7,000 deaths, the development of general models to track and predict the evolution of the outbreak, so as to guide the allocation of medical supplies and staff, is gaining notable urgency. We propose here a spatially explicit epidemic model that accounts for the dynamics of susceptible and infected individuals as well as the redistribution of Vibrio cholera, the causative agent of the disease, among different human communities. In particular, we model two spreading pathways: the advection of pathogens through hydrologic connections and the dissemination due to human mobility described by means of a gravity-like model. To this end the country has been divided into hydrologic units based on drainage directions derived from a digital terrain model. Moreover the population of each unit has been estimated from census data downscaled to 1 km x 1 km resolution via remotely sensed geomorphological information (LandScan project). The model directly accounts for the role of rainfall patterns in driving the seasonality of cholera outbreaks. The two main outbreaks in fact occurred during the rainy seasons (October and May) when extensive floodings severely worsened the sanitation conditions and, in turn, raised the risk of infection. The model capability to reproduce the spatiotemporal features of the epidemic up to date grants robustness to the foreseen future development. To this end, we generate realistic scenario of future precipitation in order to forecast possible epidemic paths up to the end of the 2013. In this context, the duration of acquired immunity, a hotly debated topic in the scientific community, emerges as a controlling factor for progression of the epidemic in the near future. The framework presented here can straightforwardly be used to evaluate the effectiveness of alternative intervention strategies like mass vaccinations
Computational algebraic geometry of epidemic models
Rodríguez Vega, Martín.
2014-06-01
Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.
Travelling Wave Solutions in Multigroup Age-Structured Epidemic Models
Ducrot, Arnaut; Magal, Pierre; Ruan, Shigui
2010-01-01
Age-structured epidemic models have been used to describe either the age of individuals or the age of infection of certain diseases and to determine how these characteristics affect the outcomes and consequences of epidemiological processes. Most results on age-structured epidemic models focus on the existence, uniqueness, and convergence to disease equilibria of solutions. In this paper we investigate the existence of travelling wave solutions in a deterministic age-structured model describing the circulation of a disease within a population of multigroups. Individuals of each group are able to move with a random walk which is modelled by the classical Fickian diffusion and are classified into two subclasses, susceptible and infective. A susceptible individual in a given group can be crisscross infected by direct contact with infective individuals of possibly any group. This process of transmission can depend upon the age of the disease of infected individuals. The goal of this paper is to provide sufficient conditions that ensure the existence of travelling wave solutions for the age-structured epidemic model. The case of two population groups is numerically investigated which applies to the crisscross transmission of feline immunodeficiency virus (FIV) and some sexual transmission diseases.
Defining epidemics in computer simulation models: How do definitions influence conclusions?
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Carolyn Orbann
2017-06-01
Full Text Available Computer models have proven to be useful tools in studying epidemic disease in human populations. Such models are being used by a broader base of researchers, and it has become more important to ensure that descriptions of model construction and data analyses are clear and communicate important features of model structure. Papers describing computer models of infectious disease often lack a clear description of how the data are aggregated and whether or not non-epidemic runs are excluded from analyses. Given that there is no concrete quantitative definition of what constitutes an epidemic within the public health literature, each modeler must decide on a strategy for identifying epidemics during simulation runs. Here, an SEIR model was used to test the effects of how varying the cutoff for considering a run an epidemic changes potential interpretations of simulation outcomes. Varying the cutoff from 0% to 15% of the model population ever infected with the illness generated significant differences in numbers of dead and timing variables. These results are important for those who use models to form public health policy, in which questions of timing or implementation of interventions might be answered using findings from computer simulation models.
On the Use of Human Mobility Proxies for Modeling Epidemics
Tizzoni, Michele; Bajardi, Paolo; Decuyper, Adeline; Kon Kam King, Guillaume; Schneider, Christian M.; Blondel, Vincent; Smoreda, Zbigniew; González, Marta C.; Colizza, Vittoria
2014-01-01
Human mobility is a key component of large-scale spatial-transmission models of infectious diseases. Correctly modeling and quantifying human mobility is critical for improving epidemic control, but may be hindered by data incompleteness or unavailability. Here we explore the opportunity of using proxies for individual mobility to describe commuting flows and predict the diffusion of an influenza-like-illness epidemic. We consider three European countries and the corresponding commuting networks at different resolution scales, obtained from (i) official census surveys, (ii) proxy mobility data extracted from mobile phone call records, and (iii) the radiation model calibrated with census data. Metapopulation models defined on these countries and integrating the different mobility layers are compared in terms of epidemic observables. We show that commuting networks from mobile phone data capture the empirical commuting patterns well, accounting for more than 87% of the total fluxes. The distributions of commuting fluxes per link from mobile phones and census sources are similar and highly correlated, however a systematic overestimation of commuting traffic in the mobile phone data is observed. This leads to epidemics that spread faster than on census commuting networks, once the mobile phone commuting network is considered in the epidemic model, however preserving to a high degree the order of infection of newly affected locations. Proxies' calibration affects the arrival times' agreement across different models, and the observed topological and traffic discrepancies among mobility sources alter the resulting epidemic invasion patterns. Results also suggest that proxies perform differently in approximating commuting patterns for disease spread at different resolution scales, with the radiation model showing higher accuracy than mobile phone data when the seed is central in the network, the opposite being observed for peripheral locations. Proxies should therefore be
Epidemic modeling in complex realities.
Colizza, Vittoria; Barthélemy, Marc; Barrat, Alain; Vespignani, Alessandro
2007-04-01
In our global world, the increasing complexity of social relations and transport infrastructures are key factors in the spread of epidemics. In recent years, the increasing availability of computer power has enabled both to obtain reliable data allowing one to quantify the complexity of the networks on which epidemics may propagate and to envision computational tools able to tackle the analysis of such propagation phenomena. These advances have put in evidence the limits of homogeneous assumptions and simple spatial diffusion approaches, and stimulated the inclusion of complex features and heterogeneities relevant in the description of epidemic diffusion. In this paper, we review recent progresses that integrate complex systems and networks analysis with epidemic modelling and focus on the impact of the various complex features of real systems on the dynamics of epidemic spreading.
Nonlinear model of epidemic spreading in a complex social network.
Kosiński, Robert A; Grabowski, A
2007-10-01
The epidemic spreading in a human society is a complex process, which can be described on the basis of a nonlinear mathematical model. In such an approach the complex and hierarchical structure of social network (which has implications for the spreading of pathogens and can be treated as a complex network), can be taken into account. In our model each individual has one of the four permitted states: susceptible, infected, infective, unsusceptible or dead. This refers to the SEIR model used in epidemiology. The state of an individual changes in time, depending on the previous state and the interactions with other individuals. The description of the interpersonal contacts is based on the experimental observations of the social relations in the community. It includes spatial localization of the individuals and hierarchical structure of interpersonal interactions. Numerical simulations were performed for different types of epidemics, giving the progress of a spreading process and typical relationships (e.g. range of epidemic in time, the epidemic curve). The spreading process has a complex and spatially chaotic character. The time dependence of the number of infective individuals shows the nonlinear character of the spreading process. We investigate the influence of the preventive vaccinations on the spreading process. In particular, for a critical value of preventively vaccinated individuals the percolation threshold is observed and the epidemic is suppressed.
Modeling Epidemics Spreading on Social Contact Networks.
Zhang, Zhaoyang; Wang, Honggang; Wang, Chonggang; Fang, Hua
2015-09-01
Social contact networks and the way people interact with each other are the key factors that impact on epidemics spreading. However, it is challenging to model the behavior of epidemics based on social contact networks due to their high dynamics. Traditional models such as susceptible-infected-recovered (SIR) model ignore the crowding or protection effect and thus has some unrealistic assumption. In this paper, we consider the crowding or protection effect and develop a novel model called improved SIR model. Then, we use both deterministic and stochastic models to characterize the dynamics of epidemics on social contact networks. The results from both simulations and real data set conclude that the epidemics are more likely to outbreak on social contact networks with higher average degree. We also present some potential immunization strategies, such as random set immunization, dominating set immunization, and high degree set immunization to further prove the conclusion.
Mechanistic movement models to understand epidemic spread.
Fofana, Abdou Moutalab; Hurford, Amy
2017-05-05
An overlooked aspect of disease ecology is considering how and why animals come into contact with one and other resulting in disease transmission. Mathematical models of disease spread frequently assume mass-action transmission, justified by stating that susceptible and infectious hosts mix readily, and foregoing any detailed description of host movement. Numerous recent studies have recorded, analysed and modelled animal movement. These movement models describe how animals move with respect to resources, conspecifics and previous movement directions and have been used to understand the conditions for the occurrence and the spread of infectious diseases when hosts perform a type of movement. Here, we summarize the effect of the different types of movement on the threshold conditions for disease spread. We identify gaps in the literature and suggest several promising directions for future research. The mechanistic inclusion of movement in epidemic models may be beneficial for the following two reasons. Firstly, the estimation of the transmission coefficient in an epidemic model is possible because animal movement data can be used to estimate the rate of contacts between conspecifics. Secondly, unsuccessful transmission events, where a susceptible host contacts an infectious host but does not become infected can be quantified. Following an outbreak, this enables disease ecologists to identify 'near misses' and to explore possible alternative epidemic outcomes given shifts in ecological or immunological parameters.This article is part of the themed issue 'Opening the black box: re-examining the ecology and evolution of parasite transmission'. © 2017 The Author(s).
Integrated travel network model for studying epidemics: Interplay between journeys and epidemic
Ruan, Zhongyuan; Wang, Chaoqing; Ming Hui, Pak; Liu, Zonghua
2015-06-01
The ease of travelling between cities has contributed much to globalization. Yet, it poses a threat on epidemic outbreaks. It is of great importance for network science and health control to understand the impact of frequent journeys on epidemics. We stress that a new framework of modelling that takes a traveller’s viewpoint is needed. Such integrated travel network (ITN) model should incorporate the diversity among links as dictated by the distances between cities and different speeds of different modes of transportation, diversity among nodes as dictated by the population and the ease of travelling due to infrastructures and economic development of a city, and round-trip journeys to targeted destinations via the paths of shortest travel times typical of human journeys. An example is constructed for 116 cities in China with populations over one million that are connected by high-speed train services and highways. Epidemic spread on the constructed network is studied. It is revealed both numerically and theoretically that the traveling speed and frequency are important factors of epidemic spreading. Depending on the infection rate, increasing the traveling speed would result in either an enhanced or suppressed epidemic, while increasing the traveling frequency enhances the epidemic spreading.
A Data-Driven Air Transportation Delay Propagation Model Using Epidemic Process Models
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B. Baspinar
2016-01-01
Full Text Available In air transport network management, in addition to defining the performance behavior of the system’s components, identification of their interaction dynamics is a delicate issue in both strategic and tactical decision-making process so as to decide which elements of the system are “controlled” and how. This paper introduces a novel delay propagation model utilizing epidemic spreading process, which enables the definition of novel performance indicators and interaction rates of the elements of the air transportation network. In order to understand the behavior of the delay propagation over the network at different levels, we have constructed two different data-driven epidemic models approximating the dynamics of the system: (a flight-based epidemic model and (b airport-based epidemic model. The flight-based epidemic model utilizing SIS epidemic model focuses on the individual flights where each flight can be in susceptible or infected states. The airport-centric epidemic model, in addition to the flight-to-flight interactions, allows us to define the collective behavior of the airports, which are modeled as metapopulations. In network model construction, we have utilized historical flight-track data of Europe and performed analysis for certain days involving certain disturbances. Through this effort, we have validated the proposed delay propagation models under disruptive events.
The SIS Model of Epidemic Spreading in a Hierarchical Social Network
International Nuclear Information System (INIS)
Grabowski, A.; Kosinski, R.A.
2005-01-01
The phenomenon of epidemic spreading in a population with a hierarchical structure of interpersonal interactions is described and investigated numerically. The SIS model with temporal immunity to a disease and a time of incubation is used. In our model spatial localization of individuals belonging to different social groups, effectiveness of different interpersonal interactions and the mobility of a contemporary community are taken into account. The structure of interpersonal connections is based on a scale-free network. The influence of the structure of the social network on typical relations characterizing the spreading process, like a range of epidemic and epidemic curves, is discussed. The probability that endemic state occurs is also calculated. Surprisingly it occurs, that less contagious diseases has greater chance to survive. The influence of preventive vaccinations on the spreading process is investigated and critical range of vaccinations that is sufficient for the suppression of an epidemic is calculated. Our results of numerical calculations are compared with the solutions of the master equation for the spreading process, and good agreement is found. (author)
Bayesian conditional-independence modeling of the AIDS epidemic in England and Wales
Gilks, Walter R.; De Angelis, Daniela; Day, Nicholas E.
We describe the use of conditional-independence modeling, Bayesian inference and Markov chain Monte Carlo, to model and project the HIV-AIDS epidemic in homosexual/bisexual males in England and Wales. Complexity in this analysis arises through selectively missing data, indirectly observed underlying processes, and measurement error. Our emphasis is on presentation and discussion of the concepts, not on the technicalities of this analysis, which can be found elsewhere [D. De Angelis, W.R. Gilks, N.E. Day, Bayesian projection of the the acquired immune deficiency syndrome epidemic (with discussion), Applied Statistics, in press].
Different Epidemic Models on Complex Networks
International Nuclear Information System (INIS)
Zhang Haifeng; Small, Michael; Fu Xinchu
2009-01-01
Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals' relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemic models on complex networks, and obtain the epidemic threshold for each case. Finally, we present numerical simulations for each case to verify our results.
Predicting extinction rates in stochastic epidemic models
International Nuclear Information System (INIS)
Schwartz, Ira B; Billings, Lora; Dykman, Mark; Landsman, Alexandra
2009-01-01
We investigate the stochastic extinction processes in a class of epidemic models. Motivated by the process of natural disease extinction in epidemics, we examine the rate of extinction as a function of disease spread. We show that the effective entropic barrier for extinction in a susceptible–infected–susceptible epidemic model displays scaling with the distance to the bifurcation point, with an unusual critical exponent. We make a direct comparison between predictions and numerical simulations. We also consider the effect of non-Gaussian vaccine schedules, and show numerically how the extinction process may be enhanced when the vaccine schedules are Poisson distributed
On the modeling of epidemics under the influence of risk perception
de Lillo, S.; Fioriti, G.; Prioriello, M. L.
An epidemic spreading model is presented in the framework of the kinetic theory of active particles. The model is characterized by the influence of risk perception which can reduce the diffusion of infection. The evolution of the system is modeled through nonlinear interactions, whose output is described by stochastic games. The results of numerical simulations are discussed for different initial conditions.
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Xiaona Leng
2017-06-01
Full Text Available Abstract This paper proposes a new nonlinear stochastic SIVS epidemic model with double epidemic hypothesis and Lévy jumps. The main purpose of this paper is to investigate the threshold dynamics of the stochastic SIVS epidemic model. By using the technique of a series of stochastic inequalities, we obtain sufficient conditions for the persistence in mean and extinction of the stochastic system and the threshold which governs the extinction and the spread of the epidemic diseases. Finally, this paper describes the results of numerical simulations investigating the dynamical effects of stochastic disturbance. Our results significantly improve and generalize the corresponding results in recent literatures. The developed theoretical methods and stochastic inequalities technique can be used to investigate the high-dimensional nonlinear stochastic differential systems.
The threshold of a stochastic avian-human influenza epidemic model with psychological effect
Zhang, Fengrong; Zhang, Xinhong
2018-02-01
In this paper, a stochastic avian-human influenza epidemic model with psychological effect in human population and saturation effect within avian population is investigated. This model describes the transmission of avian influenza among avian population and human population in random environments. For stochastic avian-only system, persistence in the mean and extinction of the infected avian population are studied. For the avian-human influenza epidemic system, sufficient conditions for the existence of an ergodic stationary distribution are obtained. Furthermore, a threshold of this stochastic model which determines the outcome of the disease is obtained. Finally, numerical simulations are given to support the theoretical results.
Epidemic spreading and global stability of an SIS model with an infective vector on complex networks
Kang, Huiyan; Fu, Xinchu
2015-10-01
In this paper, we present a new SIS model with delay on scale-free networks. The model is suitable to describe some epidemics which are not only transmitted by a vector but also spread between individuals by direct contacts. In view of the biological relevance and real spreading process, we introduce a delay to denote average incubation period of disease in a vector. By mathematical analysis, we obtain the epidemic threshold and prove the global stability of equilibria. The simulation shows the delay will effect the epidemic spreading. Finally, we investigate and compare two major immunization strategies, uniform immunization and targeted immunization.
Lismawati, Eka; Respatiwulan; Widyaningsih, Purnami
2017-06-01
The SIS epidemic model describes the pattern of disease spread with characteristics that recovered individuals can be infected more than once. The number of susceptible and infected individuals every time follows the discrete time Markov process. It can be represented by the discrete time Markov chains (DTMC) SIS. The DTMC SIS epidemic model can be developed for two pathogens in two patches. The aims of this paper are to reconstruct and to apply the DTMC SIS epidemic model with two pathogens in two patches. The model was presented as transition probabilities. The application of the model obtain that the number of susceptible individuals decreases while the number of infected individuals increases for each pathogen in each patch.
A simple model for behaviour change in epidemics
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Brauer Fred
2011-02-01
Full Text Available Abstract Background People change their behaviour during an epidemic. Infectious members of a population may reduce the number of contacts they make with other people because of the physical effects of their illness and possibly because of public health announcements asking them to do so in order to decrease the number of new infections, while susceptible members of the population may reduce the number of contacts they make in order to try to avoid becoming infected. Methods We consider a simple epidemic model in which susceptible and infectious members respond to a disease outbreak by reducing contacts by different fractions and analyze the effect of such contact reductions on the size of the epidemic. We assume constant fractional reductions, without attempting to consider the way in which susceptible members might respond to information about the epidemic. Results We are able to derive upper and lower bounds for the final size of an epidemic, both for simple and staged progression models. Conclusions The responses of uninfected and infected individuals in a disease outbreak are different, and this difference affects estimates of epidemic size.
Eight challenges for network epidemic models
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Lorenzo Pellis
2015-03-01
Full Text Available Networks offer a fertile framework for studying the spread of infection in human and animal populations. However, owing to the inherent high-dimensionality of networks themselves, modelling transmission through networks is mathematically and computationally challenging. Even the simplest network epidemic models present unanswered questions. Attempts to improve the practical usefulness of network models by including realistic features of contact networks and of host–pathogen biology (e.g. waning immunity have made some progress, but robust analytical results remain scarce. A more general theory is needed to understand the impact of network structure on the dynamics and control of infection. Here we identify a set of challenges that provide scope for active research in the field of network epidemic models.
Five challenges for stochastic epidemic models involving global transmission
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Tom Britton
2015-03-01
Full Text Available The most basic stochastic epidemic models are those involving global transmission, meaning that infection rates depend only on the type and state of the individuals involved, and not on their location in the population. Simple as they are, there are still several open problems for such models. For example, when will such an epidemic go extinct and with what probability (questions depending on the population being fixed, changing or growing? How can a model be defined explaining the sometimes observed scenario of frequent mid-sized epidemic outbreaks? How can evolution of the infectious agent transmission rates be modelled and fitted to data in a robust way?
Deriving a model for influenza epidemics from historical data.
Energy Technology Data Exchange (ETDEWEB)
Ray, Jaideep; Lefantzi, Sophia
2011-09-01
In this report we describe how we create a model for influenza epidemics from historical data collected from both civilian and military societies. We derive the model when the population of the society is unknown but the size of the epidemic is known. Our interest lies in estimating a time-dependent infection rate to within a multiplicative constant. The model form fitted is chosen for its similarity to published models for HIV and plague, enabling application of Bayesian techniques to discriminate among infectious agents during an emerging epidemic. We have developed models for the progression of influenza in human populations. The model is framed as a integral, and predicts the number of people who exhibit symptoms and seek care over a given time-period. The start and end of the time period form the limits of integration. The disease progression model, in turn, contains parameterized models for the incubation period and a time-dependent infection rate. The incubation period model is obtained from literature, and the parameters of the infection rate are fitted from historical data including both military and civilian populations. The calibrated infection rate models display a marked difference in which the 1918 Spanish Influenza pandemic differed from the influenza seasons in the US between 2001-2008 and the progression of H1N1 in Catalunya, Spain. The data for the 1918 pandemic was obtained from military populations, while the rest are country-wide or province-wide data from the twenty-first century. We see that the initial growth of infection in all cases were about the same; however, military populations were able to control the epidemic much faster i.e., the decay of the infection-rate curve is much higher. It is not clear whether this was because of the much higher level of organization present in a military society or the seriousness with which the 1918 pandemic was addressed. Each outbreak to which the influenza model was fitted yields a separate set of
Parameter Scaling for Epidemic Size in a Spatial Epidemic Model with Mobile Individuals.
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Chiyori T Urabe
Full Text Available In recent years, serious infectious diseases tend to transcend national borders and widely spread in a global scale. The incidence and prevalence of epidemics are highly influenced not only by pathogen-dependent disease characteristics such as the force of infection, the latent period, and the infectious period, but also by human mobility and contact patterns. However, the effect of heterogeneous mobility of individuals on epidemic outcomes is not fully understood. Here, we aim to elucidate how spatial mobility of individuals contributes to the final epidemic size in a spatial susceptible-exposed-infectious-recovered (SEIR model with mobile individuals in a square lattice. After illustrating the interplay between the mobility parameters and the other parameters on the spatial epidemic spreading, we propose an index as a function of system parameters, which largely governs the final epidemic size. The main contribution of this study is to show that the proposed index is useful for estimating how parameter scaling affects the final epidemic size. To demonstrate the effectiveness of the proposed index, we show that there is a positive correlation between the proposed index computed with the real data of human airline travels and the actual number of positive incident cases of influenza B in the entire world, implying that the growing incidence of influenza B is attributed to increased human mobility.
Stochastic population and epidemic models persistence and extinction
Allen, Linda J S
2015-01-01
This monograph provides a summary of the basic theory of branching processes for single-type and multi-type processes. Classic examples of population and epidemic models illustrate the probability of population or epidemic extinction obtained from the theory of branching processes. The first chapter develops the branching process theory, while in the second chapter two applications to population and epidemic processes of single-type branching process theory are explored. The last two chapters present multi-type branching process applications to epidemic models, and then continuous-time and continuous-state branching processes with applications. In addition, several MATLAB programs for simulating stochastic sample paths are provided in an Appendix. These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. Professor Linda Allen is a Paul Whitfield Horn Professor of Mathematics in the Department of Mathematics and Statistics ...
Epidemic as a natural process.
Koivu-Jolma, Mikko; Annila, Arto
2018-05-01
Mathematical epidemiology is a well-recognized discipline to model infectious diseases. It also provides guidance for public health officials to limit outbreaks. Nevertheless, epidemics take societies by surprise every now and then, for example, when the Ebola virus epidemic raged seemingly unrestrained in Western Africa. We provide insight to this capricious character of nature by describing the epidemic as a natural process, i.e., a phenomenon governed by thermodynamics. Our account, based on statistical mechanics of open systems, clarifies that it is impossible to predict accurately epidemic courses because everything depends on everything else. Nonetheless, the thermodynamic theory yields a comprehensive and analytical view of the epidemic. The tenet subsumes various processes in a scale-free manner from the molecular to the societal levels. The holistic view accentuates overarching procedures in arresting and eradicating epidemics. Copyright © 2018 Elsevier Inc. All rights reserved.
Modeling and Analysis of Epidemic Diffusion within Small-World Network
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Ming Liu
2012-01-01
Full Text Available To depict the rule of epidemic diffusion, two different models, the Susceptible-Exposure-Infected-Recovered-Susceptible (SEIRS model and the Susceptible-Exposure-Infected-Quarantine-Recovered-Susceptible (SEIQRS model, are proposed and analyzed within small-world network in this paper. Firstly, the epidemic diffusion models are constructed with mean-filed theory, and condition for the occurrence of disease diffusion is explored. Then, the existence and global stability of the disease-free equilibrium and the endemic equilibrium for these two complex epidemic systems are proved by differential equations knowledge and Routh-Hurwiz theory. At last, a numerical example which includes key parameters analysis and critical topic discussion is presented to test how well the proposed two models may be applied in practice. These works may provide some guidelines for decision makers when coping with epidemic diffusion controlling problems.
Cohen, N.E.; Brom, F.W.A.; Stassen, E.N.
2009-01-01
In this paper, we present and defend the theoretical framework of an empirical model to describe people’s fundamental moral attitudes (FMAs) to animals, the stratification of FMAs in society and the role of FMAs in judgment on the culling of healthy animals in an animal disease epidemic. We used
Flexible Modeling of Epidemics with an Empirical Bayes Framework
Brooks, Logan C.; Farrow, David C.; Hyun, Sangwon; Tibshirani, Ryan J.; Rosenfeld, Roni
2015-01-01
Seasonal influenza epidemics cause consistent, considerable, widespread loss annually in terms of economic burden, morbidity, and mortality. With access to accurate and reliable forecasts of a current or upcoming influenza epidemic’s behavior, policy makers can design and implement more effective countermeasures. This past year, the Centers for Disease Control and Prevention hosted the “Predict the Influenza Season Challenge”, with the task of predicting key epidemiological measures for the 2013–2014 U.S. influenza season with the help of digital surveillance data. We developed a framework for in-season forecasts of epidemics using a semiparametric Empirical Bayes framework, and applied it to predict the weekly percentage of outpatient doctors visits for influenza-like illness, and the season onset, duration, peak time, and peak height, with and without using Google Flu Trends data. Previous work on epidemic modeling has focused on developing mechanistic models of disease behavior and applying time series tools to explain historical data. However, tailoring these models to certain types of surveillance data can be challenging, and overly complex models with many parameters can compromise forecasting ability. Our approach instead produces possibilities for the epidemic curve of the season of interest using modified versions of data from previous seasons, allowing for reasonable variations in the timing, pace, and intensity of the seasonal epidemics, as well as noise in observations. Since the framework does not make strict domain-specific assumptions, it can easily be applied to some other diseases with seasonal epidemics. This method produces a complete posterior distribution over epidemic curves, rather than, for example, solely point predictions of forecasting targets. We report prospective influenza-like-illness forecasts made for the 2013–2014 U.S. influenza season, and compare the framework’s cross-validated prediction error on historical data to
Transferring the Malaria Epidemic Prediction Model to Users in East ...
International Development Research Centre (IDRC) Digital Library (Canada)
Transferring the Malaria Epidemic Prediction Model to Users in East Africa. In the highlands of East Africa, epidemic malaria is an emerging climate-related hazard that urgently needs addressing. Malaria incidence increased by 337% during the 1987 epidemic in Rwanda. In Tanzania, Uganda and Kenya, malaria incidence ...
Discrete stochastic analogs of Erlang epidemic models.
Getz, Wayne M; Dougherty, Eric R
2018-12-01
Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.
Modelling cholera epidemics: the role of waterways, human mobility and sanitation.
Mari, L; Bertuzzo, E; Righetto, L; Casagrandi, R; Gatto, M; Rodriguez-Iturbe, I; Rinaldo, A
2012-02-07
We investigate the role of human mobility as a driver for long-range spreading of cholera infections, which primarily propagate through hydrologically controlled ecological corridors. Our aim is to build a spatially explicit model of a disease epidemic, which is relevant to both social and scientific issues. We present a two-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of the pathogen Vibrio cholerae owing to host movement, described here by means of a gravity-model approach. We test our model against epidemiological data recorded during the extensive cholera outbreak occurred in the KwaZulu-Natal province of South Africa during 2000-2001. We show that long-range human movement is fundamental in quantifying otherwise unexplained inter-catchment transport of V. cholerae, thus playing a key role in the formation of regional patterns of cholera epidemics. We also show quantitatively how heterogeneously distributed drinking water supplies and sanitation conditions may affect large-scale cholera transmission, and analyse the effects of different sanitation policies.
Modelling cholera epidemics: the role of waterways, human mobility and sanitation
Mari, L.; Bertuzzo, E.; Righetto, L.; Casagrandi, R.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.
2012-01-01
We investigate the role of human mobility as a driver for long-range spreading of cholera infections, which primarily propagate through hydrologically controlled ecological corridors. Our aim is to build a spatially explicit model of a disease epidemic, which is relevant to both social and scientific issues. We present a two-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of the pathogen Vibrio cholerae owing to host movement, described here by means of a gravity-model approach. We test our model against epidemiological data recorded during the extensive cholera outbreak occurred in the KwaZulu-Natal province of South Africa during 2000–2001. We show that long-range human movement is fundamental in quantifying otherwise unexplained inter-catchment transport of V. cholerae, thus playing a key role in the formation of regional patterns of cholera epidemics. We also show quantitatively how heterogeneously distributed drinking water supplies and sanitation conditions may affect large-scale cholera transmission, and analyse the effects of different sanitation policies. PMID:21752809
A spatially explicit model for the future progression of the current Haiti cholera epidemic
Bertuzzo, E.; Mari, L.; Righetto, L.; Gatto, M.; Casagrandi, R.; Rodriguez-Iturbe, I.; Rinaldo, A.
2011-12-01
As a major cholera epidemic progresses in Haiti, and the figures of the infection, up to July 2011, climb to 385,000 cases and 5,800 deaths, the development of general models to track and predict the evolution of the outbreak, so as to guide the allocation of medical supplies and staff, is gaining notable urgency. We propose here a spatially explicit epidemic model that accounts for the dynamics of susceptible and infected individuals as well as the redistribution of textit{Vibrio cholera}, the causative agent of the disease, among different human communities. In particular, we model two spreading pathways: the advection of pathogens through hydrologic connections and the dissemination due to human mobility described by means of a gravity-like model. To this end the country has been divided into hydrologic units based on drainage directions derived from a digital terrain model. Moreover the population of each unit has been estimated from census data downscaled to 1 km x 1 km resolution via remotely sensed geomorphological information (LandScan texttrademark project). The model directly account for the role of rainfall patterns in driving the seasonality of cholera outbreaks. The two main outbreaks in fact occurred during the rainy seasons (October and May) when extensive floodings severely worsened the sanitation conditions and, in turn, raised the risk of infection. The model capability to reproduce the spatiotemporal features of the epidemic up to date grants robustness to the foreseen future development. In this context, the duration of acquired immunity, a hotly debated topic in the scientific community, emerges as a controlling factor for progression of the epidemic in the near future. The framework presented here can straightforwardly be used to evaluate the effectiveness of alternative intervention strategies like mass vaccinations, clean water supply and educational campaigns, thus emerging as an essential component of the control of future cholera
Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment
Khan, Muhammad Altaf; Khan, Yasir; Islam, Saeed
2018-03-01
In this paper, we describe the dynamics of an SEIR epidemic model with saturated incidence, treatment function, and optimal control. Rigorous mathematical results have been established for the model. The stability analysis of the model is investigated and found that the model is locally asymptotically stable when R0 1. The proposed model may possess a backward bifurcation. The optimal control problem is designed and obtained their necessary results. Numerical results have been presented for justification of theoretical results.
Fernández-Carrión, E; Ivorra, B; Martínez-López, B; Ramos, A M; Sánchez-Vizcaíno, J M
2016-04-01
Be-FAST is a computer program based on a time-spatial stochastic spread mathematical model for studying the transmission of infectious livestock diseases within and between farms. The present work describes a new module integrated into Be-FAST to model the economic consequences of the spreading of classical swine fever (CSF) and other infectious livestock diseases within and between farms. CSF is financially one of the most damaging diseases in the swine industry worldwide. Specifically in Spain, the economic costs in the two last CSF epidemics (1997 and 2001) reached jointly more than 108 million euros. The present analysis suggests that severe CSF epidemics are associated with significant economic costs, approximately 80% of which are related to animal culling. Direct costs associated with control measures are strongly associated with the number of infected farms, while indirect costs are more strongly associated with epidemic duration. The economic model has been validated with economic information around the last outbreaks in Spain. These results suggest that our economic module may be useful for analysing and predicting economic consequences of livestock disease epidemics. Copyright © 2016 Elsevier B.V. All rights reserved.
Modelling the dynamics of nonendemic epidemics
International Nuclear Information System (INIS)
Ramani, A.; Grammaticos, B.; Satsuma, J.
2009-01-01
We present two models for an epidemic where the individuals are infective over a fixed period of time and which never becomes endemic i.e., no infective individuals remain after the epidemic has run its course. The first model is based on a delay-difference scheme. We show that, as a function of the delay (which corresponds to the period of infectiveness) the percentage of non-infected population varies over a wide range. We present also a variant of our model where the recovery rate follows a Poisson law and obtain a discrete version of the SIR model. We estimate the percentage of non-infected population in the two models, show that they lead to almost the same values and present an explanation of this fact. The second model is based on the assumption that the infection is spread by carriers. Under the hypothesis that the carriers are relatively long-lived, and that the number of the infected ones is a relatively small fraction of the total population of potential carriers, we show that the model reduces to the same version of the discrete SIR obtained by our first model.
Modeling age-specific mortality for countries with generalized HIV epidemics.
Directory of Open Access Journals (Sweden)
David J Sharrow
Full Text Available In a given population the age pattern of mortality is an important determinant of total number of deaths, age structure, and through effects on age structure, the number of births and thereby growth. Good mortality models exist for most populations except those experiencing generalized HIV epidemics and some developing country populations. The large number of deaths concentrated at very young and adult ages in HIV-affected populations produce a unique 'humped' age pattern of mortality that is not reproduced by any existing mortality models. Both burden of disease reporting and population projection methods require age-specific mortality rates to estimate numbers of deaths and produce plausible age structures. For countries with generalized HIV epidemics these estimates should take into account the future trajectory of HIV prevalence and its effects on age-specific mortality. In this paper we present a parsimonious model of age-specific mortality for countries with generalized HIV/AIDS epidemics.The model represents a vector of age-specific mortality rates as the weighted sum of three independent age-varying components. We derive the age-varying components from a Singular Value Decomposition of the matrix of age-specific mortality rate schedules. The weights are modeled as a function of HIV prevalence and one of three possible sets of inputs: life expectancy at birth, a measure of child mortality, or child mortality with a measure of adult mortality. We calibrate the model with 320 five-year life tables for each sex from the World Population Prospects 2010 revision that come from the 40 countries of the world that have and are experiencing a generalized HIV epidemic. Cross validation shows that the model is able to outperform several existing model life table systems.We present a flexible, parsimonious model of age-specific mortality for countries with generalized HIV epidemics. Combined with the outputs of existing epidemiological and
PREDICTION OF DENGUE FEVER EPIDEMIC SPREADING USING DYNAMICS TRANSMISSION VECTOR MODEL
Directory of Open Access Journals (Sweden)
Retno Widyaningrum
2014-05-01
Full Text Available Increasing number of dengue cases in Surabaya shows that its city has high potential of dengue fever epidemic. Although some policies were designed by Surabaya Health Department, such as fogging and mosquito’s nest eradication, but these efforts still out of target because of inaccurate predictions. Ineffectiveness eradication of dengue fever epidemic is caused by lack of information and knowledge on environmental conditions in Surabaya. Developing spread and prediction system to minimize dengue fever epidemic is necessary to be conducted immediately. Spread and prediction system can improve eradication and prevention accuracy. The transmission dynamics vector simulation will be used as an approach to draw a complex system ofmosquito life cycle in which involve a lot offactors. Dynamics transmission model used to build model in mosquito model (oviposition rate and pre adult mosquito, infected and death cases in dengue fever. The model of mosquito and infected population can represent system. The output of this research is website of spread and prediction system of dengue fever epidemics to predict growth rate of Aedes Aegypti mosquito, infected, and death population because of dengue fever epidemics. The deviation of infected population is 0,519. The model of death cases in dengue fever is less precision with the deviation 1,229. Death cases model need improvement by adding some variables that influence to dengue fever death cases. Spread ofdengue fever prediction will help the government, health department to decide the best policies in minimizing the spread ofdengue fever epidemics.
The prediction of epidemics through mathematical modeling.
Schaus, Catherine
2014-01-01
Mathematical models may be resorted to in an endeavor to predict the development of epidemics. The SIR model is one of the applications. Still too approximate, the use of statistics awaits more data in order to come closer to reality.
Invited review: Epidemics on social networks
Directory of Open Access Journals (Sweden)
M. N. Kuperman
2013-01-01
Full Text Available Since its first formulations almost a century ago, mathematical models fordisease spreading contributed to understand, evaluate and control the epidemic processes.They promoted a dramatic change in how epidemiologists thought of the propagation of infectious diseases.In the last decade, when the traditional epidemiological models seemed to be exhausted, new types of models were developed.These new models incorporated concepts from graph theory to describe and model the underlying social structure.Many of these works merely produced a more detailed extension of the previous results, but some otherstriggered a completely new paradigm in the mathematical study of epidemic processes. In this review, we will introduce the basicconcepts of epidemiology, epidemic modeling and networks, to finally provide a brief description of the mostrelevant results in the field.Received: 6 April 2013, Accepted: 3 June 2013; Edited by: G. Mindlin; DOI: http://dx.doi.org/10.4279/PIP.050003Cite as: M N Kuperman, Papers in Physics 5, 050003 (2013
Evaluating neighborhood structures for modeling intercity diffusion of large-scale dengue epidemics.
Wen, Tzai-Hung; Hsu, Ching-Shun; Hu, Ming-Che
2018-05-03
Dengue fever is a vector-borne infectious disease that is transmitted by contact between vector mosquitoes and susceptible hosts. The literature has addressed the issue on quantifying the effect of individual mobility on dengue transmission. However, there are methodological concerns in the spatial regression model configuration for examining the effect of intercity-scale human mobility on dengue diffusion. The purposes of the study are to investigate the influence of neighborhood structures on intercity epidemic progression from pre-epidemic to epidemic periods and to compare definitions of different neighborhood structures for interpreting the spread of dengue epidemics. We proposed a framework for assessing the effect of model configurations on dengue incidence in 2014 and 2015, which were the most severe outbreaks in 70 years in Taiwan. Compared with the conventional model configuration in spatial regression analysis, our proposed model used a radiation model, which reflects population flow between townships, as a spatial weight to capture the structure of human mobility. The results of our model demonstrate better model fitting performance, indicating that the structure of human mobility has better explanatory power in dengue diffusion than the geometric structure of administration boundaries and geographic distance between centroids of cities. We also identified spatial-temporal hierarchy of dengue diffusion: dengue incidence would be influenced by its immediate neighboring townships during pre-epidemic and epidemic periods, and also with more distant neighbors (based on mobility) in pre-epidemic periods. Our findings suggest that the structure of population mobility could more reasonably capture urban-to-urban interactions, which implies that the hub cities could be a "bridge" for large-scale transmission and make townships that immediately connect to hub cities more vulnerable to dengue epidemics.
Networked SIS Epidemics With Awareness
Paarporn, Keith
2017-07-20
We study a susceptible-infected-susceptible epidemic process over a static contact network where the nodes have partial information about the epidemic state. They react by limiting their interactions with their neighbors when they believe the epidemic is currently prevalent. A node\\'s awareness is weighted by the fraction of infected neighbors in their social network, and a global broadcast of the fraction of infected nodes in the entire network. The dynamics of the benchmark (no awareness) and awareness models are described by discrete-time Markov chains, from which mean-field approximations (MFAs) are derived. The states of the MFA are interpreted as the nodes\\' probabilities of being infected. We show a sufficient condition for the existence of a
Epidemics in interconnected small-world networks.
Liu, Meng; Li, Daqing; Qin, Pengju; Liu, Chaoran; Wang, Huijuan; Wang, Feilong
2015-01-01
Networks can be used to describe the interconnections among individuals, which play an important role in the spread of disease. Although the small-world effect has been found to have a significant impact on epidemics in single networks, the small-world effect on epidemics in interconnected networks has rarely been considered. Here, we study the susceptible-infected-susceptible (SIS) model of epidemic spreading in a system comprising two interconnected small-world networks. We find that the epidemic threshold in such networks decreases when the rewiring probability of the component small-world networks increases. When the infection rate is low, the rewiring probability affects the global steady-state infection density, whereas when the infection rate is high, the infection density is insensitive to the rewiring probability. Moreover, epidemics in interconnected small-world networks are found to spread at different velocities that depend on the rewiring probability.
Epidemics in interconnected small-world networks.
Directory of Open Access Journals (Sweden)
Meng Liu
Full Text Available Networks can be used to describe the interconnections among individuals, which play an important role in the spread of disease. Although the small-world effect has been found to have a significant impact on epidemics in single networks, the small-world effect on epidemics in interconnected networks has rarely been considered. Here, we study the susceptible-infected-susceptible (SIS model of epidemic spreading in a system comprising two interconnected small-world networks. We find that the epidemic threshold in such networks decreases when the rewiring probability of the component small-world networks increases. When the infection rate is low, the rewiring probability affects the global steady-state infection density, whereas when the infection rate is high, the infection density is insensitive to the rewiring probability. Moreover, epidemics in interconnected small-world networks are found to spread at different velocities that depend on the rewiring probability.
Stochastic epidemic-type model with enhanced connectivity: exact solution
International Nuclear Information System (INIS)
Williams, H T; Mazilu, I; Mazilu, D A
2012-01-01
We present an exact analytical solution to a one-dimensional model of the susceptible–infected–recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming the master equation via a quantum spin operator formulation. We calculate exactly the time-dependent density of infected, recovered and susceptible populations for random initial conditions. Our results compare well with those of previous work, validating the model as a useful tool for additional and extended studies in this important area. Our model also provides exact solutions for the n-point correlation functions, and can be extended to more complex epidemic-type models
A Weighted Configuration Model and Inhomogeneous Epidemics
Britton, Tom; Deijfen, Maria; Liljeros, Fredrik
2011-12-01
A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight according to a distribution that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create edges. An expression for the threshold for the appearance of a giant component in the resulting graph is derived using results on multi-type branching processes. The same technique also gives an expression for the basic reproduction number for an epidemic on the graph where the probability that a certain edge is used for transmission is a function of the edge weight (reflecting how closely `connected' the corresponding vertices are). It is demonstrated that, if vertices with large degree tend to have large (small) weights on their edges and if the transmission probability increases with the edge weight, then it is easier (harder) for the epidemic to take off compared to a randomized epidemic with the same degree and weight distribution. A recipe for calculating the probability of a large outbreak in the epidemic and the size of such an outbreak is also given. Finally, the model is fitted to three empirical weighted networks of importance for the spread of contagious diseases and it is shown that R 0 can be substantially over- or underestimated if the correlation between degree and weight is not taken into account.
The threshold of a stochastic delayed SIR epidemic model with vaccination
Liu, Qun; Jiang, Daqing
2016-11-01
In this paper, we study the threshold dynamics of a stochastic delayed SIR epidemic model with vaccination. We obtain sufficient conditions for extinction and persistence in the mean of the epidemic. The threshold between persistence in the mean and extinction of the stochastic system is also obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number Rbar0 of the deterministic system. Results show that time delay has important effects on the persistence and extinction of the epidemic.
The threshold of a stochastic delayed SIR epidemic model with temporary immunity
Liu, Qun; Chen, Qingmei; Jiang, Daqing
2016-05-01
This paper is concerned with the asymptotic properties of a stochastic delayed SIR epidemic model with temporary immunity. Sufficient conditions for extinction and persistence in the mean of the epidemic are established. The threshold between persistence in the mean and extinction of the epidemic is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.
FluTE, a publicly available stochastic influenza epidemic simulation model.
Directory of Open Access Journals (Sweden)
Dennis L Chao
2010-01-01
Full Text Available Mathematical and computer models of epidemics have contributed to our understanding of the spread of infectious disease and the measures needed to contain or mitigate them. To help prepare for future influenza seasonal epidemics or pandemics, we developed a new stochastic model of the spread of influenza across a large population. Individuals in this model have realistic social contact networks, and transmission and infections are based on the current state of knowledge of the natural history of influenza. The model has been calibrated so that outcomes are consistent with the 1957/1958 Asian A(H2N2 and 2009 pandemic A(H1N1 influenza viruses. We present examples of how this model can be used to study the dynamics of influenza epidemics in the United States and simulate how to mitigate or delay them using pharmaceutical interventions and social distancing measures. Computer simulation models play an essential role in informing public policy and evaluating pandemic preparedness plans. We have made the source code of this model publicly available to encourage its use and further development.
FluTE, a publicly available stochastic influenza epidemic simulation model.
Chao, Dennis L; Halloran, M Elizabeth; Obenchain, Valerie J; Longini, Ira M
2010-01-29
Mathematical and computer models of epidemics have contributed to our understanding of the spread of infectious disease and the measures needed to contain or mitigate them. To help prepare for future influenza seasonal epidemics or pandemics, we developed a new stochastic model of the spread of influenza across a large population. Individuals in this model have realistic social contact networks, and transmission and infections are based on the current state of knowledge of the natural history of influenza. The model has been calibrated so that outcomes are consistent with the 1957/1958 Asian A(H2N2) and 2009 pandemic A(H1N1) influenza viruses. We present examples of how this model can be used to study the dynamics of influenza epidemics in the United States and simulate how to mitigate or delay them using pharmaceutical interventions and social distancing measures. Computer simulation models play an essential role in informing public policy and evaluating pandemic preparedness plans. We have made the source code of this model publicly available to encourage its use and further development.
Recurrent dynamics in an epidemic model due to stimulated bifurcation crossovers
Energy Technology Data Exchange (ETDEWEB)
Juanico, Drandreb Earl [Department of Mathematics, Ateneo de Manila University, Loyola Heights, Quezon City, Philippines 1108 (Philippines); National Institute of Physics, University of the Philippines, Diliman, Quezon City, Philippines 1101 (Philippines)
2015-05-15
Epidemics are known to persist in the form of recurrence cycles. Despite intervention efforts through vaccination and targeted social distancing, peaks of activity for infectious diseases like influenza reappear over time. Analysis of a stochastic model is here undertaken to explore a proposed cycle-generating mechanism – the bifurcation crossover. Time series from simulations of the model exhibit oscillations similar to the temporal signature of influenza activity. Power-spectral density indicates a resonant frequency, which corresponds to the annual seasonality of influenza in temperate zones. The study finds that intervention actions influence the extinguishability of epidemic activity. Asymptotic solution to a backward Kolmogorov equation corresponds to a mean extinction time that is a function of both intervention efficacy and population size. Intervention efficacy must be greater than a certain threshold to increase the chances of extinguishing the epidemic. Agreement of the model with several phenomenological features of epidemic cycles lends to it a tractability that may serve as early warning of imminent outbreaks.
Recurrent dynamics in an epidemic model due to stimulated bifurcation crossovers
International Nuclear Information System (INIS)
Juanico, Drandreb Earl
2015-01-01
Epidemics are known to persist in the form of recurrence cycles. Despite intervention efforts through vaccination and targeted social distancing, peaks of activity for infectious diseases like influenza reappear over time. Analysis of a stochastic model is here undertaken to explore a proposed cycle-generating mechanism – the bifurcation crossover. Time series from simulations of the model exhibit oscillations similar to the temporal signature of influenza activity. Power-spectral density indicates a resonant frequency, which corresponds to the annual seasonality of influenza in temperate zones. The study finds that intervention actions influence the extinguishability of epidemic activity. Asymptotic solution to a backward Kolmogorov equation corresponds to a mean extinction time that is a function of both intervention efficacy and population size. Intervention efficacy must be greater than a certain threshold to increase the chances of extinguishing the epidemic. Agreement of the model with several phenomenological features of epidemic cycles lends to it a tractability that may serve as early warning of imminent outbreaks
Sensitivity analysis of an individual-based model for simulation of influenza epidemics.
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Elaine O Nsoesie
Full Text Available Individual-based epidemiology models are increasingly used in the study of influenza epidemics. Several studies on influenza dynamics and evaluation of intervention measures have used the same incubation and infectious period distribution parameters based on the natural history of influenza. A sensitivity analysis evaluating the influence of slight changes to these parameters (in addition to the transmissibility would be useful for future studies and real-time modeling during an influenza pandemic.In this study, we examined individual and joint effects of parameters and ranked parameters based on their influence on the dynamics of simulated epidemics. We also compared the sensitivity of the model across synthetic social networks for Montgomery County in Virginia and New York City (and surrounding metropolitan regions with demographic and rural-urban differences. In addition, we studied the effects of changing the mean infectious period on age-specific epidemics. The research was performed from a public health standpoint using three relevant measures: time to peak, peak infected proportion and total attack rate. We also used statistical methods in the design and analysis of the experiments. The results showed that: (i minute changes in the transmissibility and mean infectious period significantly influenced the attack rate; (ii the mean of the incubation period distribution appeared to be sufficient for determining its effects on the dynamics of epidemics; (iii the infectious period distribution had the strongest influence on the structure of the epidemic curves; (iv the sensitivity of the individual-based model was consistent across social networks investigated in this study and (v age-specific epidemics were sensitive to changes in the mean infectious period irrespective of the susceptibility of the other age groups. These findings suggest that small changes in some of the disease model parameters can significantly influence the uncertainty
Stability analysis of an HIV/AIDS epidemic model with treatment
Cai, Liming; Li, Xuezhi; Ghosh, Mini; Guo, Baozhu
2009-07-01
An HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number [real]0. If [real]01. Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.
Epidemic spreading with activity-driven awareness diffusion on multiplex network.
Guo, Quantong; Lei, Yanjun; Jiang, Xin; Ma, Yifang; Huo, Guanying; Zheng, Zhiming
2016-04-01
There has been growing interest in exploring the interplay between epidemic spreading with human response, since it is natural for people to take various measures when they become aware of epidemics. As a proper way to describe the multiple connections among people in reality, multiplex network, a set of nodes interacting through multiple sets of edges, has attracted much attention. In this paper, to explore the coupled dynamical processes, a multiplex network with two layers is built. Specifically, the information spreading layer is a time varying network generated by the activity driven model, while the contagion layer is a static network. We extend the microscopic Markov chain approach to derive the epidemic threshold of the model. Compared with extensive Monte Carlo simulations, the method shows high accuracy for the prediction of the epidemic threshold. Besides, taking different spreading models of awareness into consideration, we explored the interplay between epidemic spreading with awareness spreading. The results show that the awareness spreading can not only enhance the epidemic threshold but also reduce the prevalence of epidemics. When the spreading of awareness is defined as susceptible-infected-susceptible model, there exists a critical value where the dynamical process on the awareness layer can control the onset of epidemics; while if it is a threshold model, the epidemic threshold emerges an abrupt transition with the local awareness ratio α approximating 0.5. Moreover, we also find that temporal changes in the topology hinder the spread of awareness which directly affect the epidemic threshold, especially when the awareness layer is threshold model. Given that the threshold model is a widely used model for social contagion, this is an important and meaningful result. Our results could also lead to interesting future research about the different time-scales of structural changes in multiplex networks.
Epidemic spreading with activity-driven awareness diffusion on multiplex network
Guo, Quantong; Lei, Yanjun; Jiang, Xin; Ma, Yifang; Huo, Guanying; Zheng, Zhiming
2016-04-01
There has been growing interest in exploring the interplay between epidemic spreading with human response, since it is natural for people to take various measures when they become aware of epidemics. As a proper way to describe the multiple connections among people in reality, multiplex network, a set of nodes interacting through multiple sets of edges, has attracted much attention. In this paper, to explore the coupled dynamical processes, a multiplex network with two layers is built. Specifically, the information spreading layer is a time varying network generated by the activity driven model, while the contagion layer is a static network. We extend the microscopic Markov chain approach to derive the epidemic threshold of the model. Compared with extensive Monte Carlo simulations, the method shows high accuracy for the prediction of the epidemic threshold. Besides, taking different spreading models of awareness into consideration, we explored the interplay between epidemic spreading with awareness spreading. The results show that the awareness spreading can not only enhance the epidemic threshold but also reduce the prevalence of epidemics. When the spreading of awareness is defined as susceptible-infected-susceptible model, there exists a critical value where the dynamical process on the awareness layer can control the onset of epidemics; while if it is a threshold model, the epidemic threshold emerges an abrupt transition with the local awareness ratio α approximating 0.5. Moreover, we also find that temporal changes in the topology hinder the spread of awareness which directly affect the epidemic threshold, especially when the awareness layer is threshold model. Given that the threshold model is a widely used model for social contagion, this is an important and meaningful result. Our results could also lead to interesting future research about the different time-scales of structural changes in multiplex networks.
Steady States in SIRS Epidemical Model of Mobile Individuals
International Nuclear Information System (INIS)
Zhang Duanming; He Minhua; Yu Xiaoling; Pan Guijun; Sun Hongzhang; Su Xiangying; Sun Fan; Yin Yanping; Li Rui; Liu Dan
2006-01-01
We consider an epidemical model within socially interacting mobile individuals to study the behaviors of steady states of epidemic propagation in 2D networks. Using mean-field approximation and large scale simulations, we recover the usual epidemic behavior with critical thresholds δ c and p c below which infectious disease dies out. For the population density δ far above δ c , it is found that there is linear relationship between contact rate λ and the population density δ in the main. At the same time, the result obtained from mean-field approximation is compared with our numerical result, and it is found that these two results are similar by and large but not completely the same.
Steady States in SIRS Epidemical Model of Mobile Individuals
Institute of Scientific and Technical Information of China (English)
ZHANG Duan-Ming; LIU Dan; HE Min-Hua; YU Xiao-Ling; PAN Gui-Jun; SUN Hong-Zhang; SU Xiang-Ying; SUN Fan; YIN Yan-Ping; LI Rui
2006-01-01
We consider an epidemical model within socially interacting mobile individuals to study the behaviors of steady statesof epidemic propagation in 2D networks. Using mean-field approximation and large scale simulations, we recover the usual epidemic behavior with critical thresholds δc and pc below which infectious disease dies out. For the population density δ far above δc, it is found that there is linear relationship between contact rate λ and the population density δ in the main. At the same time, the result obtained from mean-field approximation is compared with our numerical result, and it is found that these two results are similar by and large but not completely the same.
The effect of awareness on networked SIS epidemics
Paarporn, Keith
2017-01-05
We study an SIS epidemic model over an arbitrary fixed network topology where the n agents, or nodes of the network, have partial information about the epidemic state. The agents react by distancing themselves from their neighbors when they believe the epidemic is currently prevalent. An agent\\'s awareness is weighted from three sources of information: the fraction of infected neighbors in their contact network, their social network, and a global broadcast of the fraction of infected nodes in the entire network. The dynamics of the benchmark (no awareness) and awareness models are described by discrete-time 2-state Markov chains. Through a coupling technique, we establish monotonicity properties between the benchmark and awareness models. Particularly, we show that the expectation of any increasing random variable on the space of sample paths, e.g. eradication time or total infections, is lower for the awareness model. In addition, we give a characterization for this difference of expectations in terms of the coupling distribution. In simulations, we evaluate how different sources of information affect the spread of an epidemic.
Moraes, Alvaro
2015-01-01
Epidemics have shaped, sometimes more than wars and natural disasters, demo- graphic aspects of human populations around the world, their health habits and their economies. Ebola and the Middle East Respiratory Syndrome (MERS) are clear and current examples of potential hazards at planetary scale. During the spread of an epidemic disease, there are phenomena, like the sudden extinction of the epidemic, that can not be captured by deterministic models. As a consequence, stochastic models have been proposed during the last decades. A typical forward problem in the stochastic setting could be the approximation of the expected number of infected individuals found in one month from now. On the other hand, a typical inverse problem could be, given a discretely observed set of epidemiological data, infer the transmission rate of the epidemic or its basic reproduction number. Markovian epidemic models are stochastic models belonging to a wide class of pure jump processes known as Stochastic Reaction Networks (SRNs), that are intended to describe the time evolution of interacting particle systems where one particle interacts with the others through a finite set of reaction channels. SRNs have been mainly developed to model biochemical reactions but they also have applications in neural networks, virus kinetics, and dynamics of social networks, among others. 4 This PhD thesis is focused on novel fast simulation algorithms and statistical inference methods for SRNs. Our novel Multi-level Monte Carlo (MLMC) hybrid simulation algorithms provide accurate estimates of expected values of a given observable of SRNs at a prescribed final time. They are designed to control the global approximation error up to a user-selected accuracy and up to a certain confidence level, and with near optimal computational work. We also present novel dual-weighted residual expansions for fast estimation of weak and strong errors arising from the MLMC methodology. Regarding the statistical inference
A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis
Directory of Open Access Journals (Sweden)
Linda J.S. Allen
2017-05-01
Full Text Available Some mathematical methods for formulation and numerical simulation of stochastic epidemic models are presented. Specifically, models are formulated for continuous-time Markov chains and stochastic differential equations. Some well-known examples are used for illustration such as an SIR epidemic model and a host-vector malaria model. Analytical methods for approximating the probability of a disease outbreak are also discussed. Keywords: Branching process, Continuous-time Markov chain, Minor outbreak, Stochastic differential equation, 2000 MSC: 60H10, 60J28, 92D30
Outbreak or Epidemic? How Obama's Language Choice Transformed the Ebola Outbreak Into an Epidemic.
Gesser-Edelsburg, Anat; Shir-Raz, Yaffa; Bar-Lev, Oshrat Sassoni; James, James J; Green, Manfred S
2016-08-01
Our aim was to examine in what terms leading newspapers' online sites described the current Ebola crisis. We employed a quantitative content analysis of terms attributed to Ebola. We found and analyzed 582 articles published between March 23 and September 30, 2014, on the online websites of 3 newspapers: The New York Times, Daily Mail, and Ynet. Our theoretical framework drew from the fields of health communication and emerging infectious disease communication, including such concepts as framing media literacy, risk signatures, and mental models. We found that outbreak and epidemic were used interchangeably in the articles. From September 16, 2014, onward, epidemic predominated, corresponding to when President Barack Obama explicitly referred to Ebola as an epidemic. Prior to Obama's speech, 86.8% of the articles (323) used the term outbreak and only 8.6% (32) used the term epidemic. Subsequently, both terms were used almost the same amount: 53.8% of the articles (113) used the term outbreak and 53.3% (112) used the term epidemic. Effective communication is crucial during public health emergencies such as Ebola, because language framing affects the decision-making process of social judgments and actions. The choice of one term (outbreak) over another (epidemic) can create different conceptualizations of the disease, thereby influencing the risk signature. (Disaster Med Public Health Preparedness. 2016;10:669-673).
Directory of Open Access Journals (Sweden)
Carlos Polanco
2013-01-01
Full Text Available A severe respiratory disease epidemic outbreak correlates with a high demand of specific supplies and specialized personnel to hold it back in a wide region or set of regions; these supplies would be beds, storage areas, hemodynamic monitors, and mechanical ventilators, as well as physicians, respiratory technicians, and specialized nurses. We describe an online cumulative sum based model named Overcrowd-Severe-Respiratory-Disease-Index based on the Modified Overcrowd Index that simultaneously monitors and informs the demand of those supplies and personnel in a healthcare network generating early warnings of severe respiratory disease epidemic outbreaks through the interpretation of such variables. A post hoc historical archive is generated, helping physicians in charge to improve the transit and future allocation of supplies in the entire hospital network during the outbreak. The model was thoroughly verified in a virtual scenario, generating multiple epidemic outbreaks in a 6-year span for a 13-hospital network. When it was superimposed over the H1N1 influenza outbreak census (2008–2010 taken by the National Institute of Medical Sciences and Nutrition Salvador Zubiran in Mexico City, it showed that it is an effective algorithm to notify early warnings of severe respiratory disease epidemic outbreaks with a minimal rate of false alerts.
Castañón-González, Jorge Alberto; Macías, Alejandro E.; Samaniego, José Lino; Buhse, Thomas; Villanueva-Martínez, Sebastián
2013-01-01
A severe respiratory disease epidemic outbreak correlates with a high demand of specific supplies and specialized personnel to hold it back in a wide region or set of regions; these supplies would be beds, storage areas, hemodynamic monitors, and mechanical ventilators, as well as physicians, respiratory technicians, and specialized nurses. We describe an online cumulative sum based model named Overcrowd-Severe-Respiratory-Disease-Index based on the Modified Overcrowd Index that simultaneously monitors and informs the demand of those supplies and personnel in a healthcare network generating early warnings of severe respiratory disease epidemic outbreaks through the interpretation of such variables. A post hoc historical archive is generated, helping physicians in charge to improve the transit and future allocation of supplies in the entire hospital network during the outbreak. The model was thoroughly verified in a virtual scenario, generating multiple epidemic outbreaks in a 6-year span for a 13-hospital network. When it was superimposed over the H1N1 influenza outbreak census (2008–2010) taken by the National Institute of Medical Sciences and Nutrition Salvador Zubiran in Mexico City, it showed that it is an effective algorithm to notify early warnings of severe respiratory disease epidemic outbreaks with a minimal rate of false alerts. PMID:24069063
Epidemic spreading in a hierarchical social network.
Grabowski, A; Kosiński, R A
2004-09-01
A model of epidemic spreading in a population with a hierarchical structure of interpersonal interactions is described and investigated numerically. The structure of interpersonal connections is based on a scale-free network. Spatial localization of individuals belonging to different social groups, and the mobility of a contemporary community, as well as the effectiveness of different interpersonal interactions, are taken into account. Typical relations characterizing the spreading process, like a range of epidemic and epidemic curves, are discussed. The influence of preventive vaccinations on the spreading process is investigated. The critical value of preventively vaccinated individuals that is sufficient for the suppression of an epidemic is calculated. Our results are compared with solutions of the master equation for the spreading process and good agreement of the character of this process is found.
Woo, Jiyoung; Chen, Hsinchun
2016-01-01
As social media has become more prevalent, its influence on business, politics, and society has become significant. Due to easy access and interaction between large numbers of users, information diffuses in an epidemic style on the web. Understanding the mechanisms of information diffusion through these new publication methods is important for political and marketing purposes. Among social media, web forums, where people in online communities disseminate and receive information, provide a good environment for examining information diffusion. In this paper, we model topic diffusion in web forums using the epidemiology model, the susceptible-infected-recovered (SIR) model, frequently used in previous research to analyze both disease outbreaks and knowledge diffusion. The model was evaluated on a large longitudinal dataset from the web forum of a major retail company and from a general political discussion forum. The fitting results showed that the SIR model is a plausible model to describe the diffusion process of a topic. This research shows that epidemic models can expand their application areas to topic discussion on the web, particularly social media such as web forums.
A stochastic modeling of recurrent measles epidemic | Kassem ...
African Journals Online (AJOL)
A simple stochastic mathematical model is developed and investigated for the dynamics of measles epidemic. The model, which is a multi-dimensional diffusion process, includes susceptible individuals, latent (exposed), infected and removed individuals. Stochastic effects are assumed to arise in the process of infection of ...
Frasso, Gianluca; Lambert, Philippe
2016-10-01
SummaryThe 2014 Ebola outbreak in Sierra Leone is analyzed using a susceptible-exposed-infectious-removed (SEIR) epidemic compartmental model. The discrete time-stochastic model for the epidemic evolution is coupled to a set of ordinary differential equations describing the dynamics of the expected proportions of subjects in each epidemic state. The unknown parameters are estimated in a Bayesian framework by combining data on the number of new (laboratory confirmed) Ebola cases reported by the Ministry of Health and prior distributions for the transition rates elicited using information collected by the WHO during the follow-up of specific Ebola cases. The time-varying disease transmission rate is modeled in a flexible way using penalized B-splines. Our framework represents a valuable stochastic tool for the study of an epidemic dynamic even when only irregularly observed and possibly aggregated data are available. Simulations and the analysis of the 2014 Sierra Leone Ebola data highlight the merits of the proposed methodology. In particular, the flexible modeling of the disease transmission rate makes the estimation of the effective reproduction number robust to the misspecification of the initial epidemic states and to underreporting of the infectious cases. © The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Basic definitions for discrete modeling of computer worms epidemics
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Pedro Guevara López
2015-01-01
Full Text Available The information technologies have evolved in such a way that communication between computers or hosts has become common, so much that the worldwide organization (governments and corporations depends on it; what could happen if these computers stop working for a long time is catastrophic. Unfortunately, networks are attacked by malware such as viruses and worms that could collapse the system. This has served as motivation for the formal study of computer worms and epidemics to develop strategies for prevention and protection; this is why in this paper, before analyzing epidemiological models, a set of formal definitions based on set theory and functions is proposed for describing 21 concepts used in the study of worms. These definitions provide a basis for future qualitative research on the behavior of computer worms, and quantitative for the study of their epidemiological models.
López, Leonardo; Burguerner, Germán; Giovanini, Leonardo
2014-04-12
The spread of an infectious disease is determined by biological and social factors. Models based on cellular automata are adequate to describe such natural systems consisting of a massive collection of simple interacting objects. They characterize the time evolution of the global system as the emergent behaviour resulting from the interaction of the objects, whose behaviour is defined through a set of simple rules that encode the individual behaviour and the transmission dynamic. An epidemic is characterized trough an individual-based-model built upon cellular automata. In the proposed model, each individual of the population is represented by a cell of the automata. This way of modeling an epidemic situation allows to individually define the characteristic of each individual, establish different scenarios and implement control strategies. A cellular automata model to study the time evolution of a heterogeneous populations through the various stages of disease was proposed, allowing the inclusion of individual heterogeneity, geographical characteristics and social factors that determine the dynamic of the desease. Different assumptions made to built the classical model were evaluated, leading to following results: i) for low contact rate (like in quarantine process or low density population areas) the number of infective individuals is lower than other areas where the contact rate is higher, and ii) for different initial spacial distributions of infected individuals different epidemic dynamics are obtained due to its influence on the transition rate and the reproductive ratio of disease. The contact rate and spatial distributions have a central role in the spread of a disease. For low density populations the spread is very low and the number of infected individuals is lower than in highly populated areas. The spacial distribution of the population and the disease focus as well as the geographical characteristic of the area play a central role in the dynamics of the
Simulating individual-based models of epidemics in hierarchical networks
Quax, R.; Bader, D.A.; Sloot, P.M.A.
2009-01-01
Current mathematical modeling methods for the spreading of infectious diseases are too simplified and do not scale well. We present the Simulator of Epidemic Evolution in Complex Networks (SEECN), an efficient simulator of detailed individual-based models by parameterizing separate dynamics
Dynamic malware containment under an epidemic model with alert
Zhang, Tianrui; Yang, Lu-Xing; Yang, Xiaofan; Wu, Yingbo; Tang, Yuan Yan
2017-03-01
Alerting at the early stage of malware invasion turns out to be an important complement to malware detection and elimination. This paper addresses the issue of how to dynamically contain the prevalence of malware at a lower cost, provided alerting is feasible. A controlled epidemic model with alert is established, and an optimal control problem based on the epidemic model is formulated. The optimality system for the optimal control problem is derived. The structure of an optimal control for the proposed optimal control problem is characterized under some conditions. Numerical examples show that the cost-efficiency of an optimal control strategy can be enhanced by adjusting the upper and lower bounds on admissible controls.
Zakary, Omar; Rachik, Mostafa; Elmouki, Ilias
2017-08-01
First, we devise in this paper, a multi-regions discrete-time model which describes the spatial-temporal spread of an epidemic which starts from one region and enters to regions which are connected with their neighbors by any kind of anthropological movement. We suppose homogeneous Susceptible-Infected-Removed (SIR) populations, and we consider in our simulations, a grid of colored cells, which represents the whole domain affected by the epidemic while each cell can represent a sub-domain or region. Second, in order to minimize the number of infected individuals in one region, we propose an optimal control approach based on a travel-blocking vicinity strategy which aims to control only one cell by restricting movements of infected people coming from all neighboring cells. Thus, we show the influence of the optimal control approach on the controlled cell. We should also note that the cellular modeling approach we propose here, can also describes infection dynamics of regions which are not necessarily attached one to an other, even if no empty space can be viewed between cells. The theoretical method we follow for the characterization of the travel-locking optimal controls, is based on a discrete version of Pontryagin's maximum principle while the numerical approach applied to the multi-points boundary value problems we obtain here, is based on discrete progressive-regressive iterative schemes. We illustrate our modeling and control approaches by giving an example of 100 regions.
Mathematics of epidemics on networks from exact to approximate models
Kiss, István Z; Simon, Péter L
2017-01-01
This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...
Real-time characterization of partially observed epidemics using surrogate models.
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Safta, Cosmin; Ray, Jaideep; Lefantzi, Sophia; Crary, David (Applied Research Associates, Arlington, VA); Sargsyan, Khachik; Cheng, Karen (Applied Research Associates, Arlington, VA)
2011-09-01
We present a statistical method, predicated on the use of surrogate models, for the 'real-time' characterization of partially observed epidemics. Observations consist of counts of symptomatic patients, diagnosed with the disease, that may be available in the early epoch of an ongoing outbreak. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information on the dynamics of the etiologic agent in the affected population e.g., the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and epidemiological parameters are estimated as distributions using a Markov chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. In some cases, the inverse problem can be computationally expensive, primarily due to the epidemic simulator used inside the inversion algorithm. We present a method, based on replacing the epidemiological model with computationally inexpensive surrogates, that can reduce the computational time to minutes, without a significant loss of accuracy. The surrogates are created by projecting the output of an epidemiological model on a set of polynomial chaos bases; thereafter, computations involving the surrogate model reduce to evaluations of a polynomial. We find that the epidemic characterizations obtained with the surrogate models is very close to that obtained with the original model. We also find that the number of projections required to construct a surrogate model is O(10)-O(10{sup 2}) less than the number of samples required by the MCMC to construct a stationary posterior distribution; thus, depending upon the epidemiological models in question, it may be possible to omit the offline creation and caching of surrogate models, prior to their use in an inverse problem. The technique is demonstrated on synthetic data as well as
Recalibrating disease parameters for increasing realism in modeling epidemics in closed settings
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Livio Bioglio
2016-11-01
Full Text Available Abstract Background The homogeneous mixing assumption is widely adopted in epidemic modelling for its parsimony and represents the building block of more complex approaches, including very detailed agent-based models. The latter assume homogeneous mixing within schools, workplaces and households, mostly for the lack of detailed information on human contact behaviour within these settings. The recent data availability on high-resolution face-to-face interactions makes it now possible to assess the goodness of this simplified scheme in reproducing relevant aspects of the infection dynamics. Methods We consider empirical contact networks gathered in different contexts, as well as synthetic data obtained through realistic models of contacts in structured populations. We perform stochastic spreading simulations on these contact networks and in populations of the same size under a homogeneous mixing hypothesis. We adjust the epidemiological parameters of the latter in order to fit the prevalence curve of the contact epidemic model. We quantify the agreement by comparing epidemic peak times, peak values, and epidemic sizes. Results Good approximations of the peak times and peak values are obtained with the homogeneous mixing approach, with a median relative difference smaller than 20 % in all cases investigated. Accuracy in reproducing the peak time depends on the setting under study, while for the peak value it is independent of the setting. Recalibration is found to be linear in the epidemic parameters used in the contact data simulations, showing changes across empirical settings but robustness across groups and population sizes. Conclusions An adequate rescaling of the epidemiological parameters can yield a good agreement between the epidemic curves obtained with a real contact network and a homogeneous mixing approach in a population of the same size. The use of such recalibrated homogeneous mixing approximations would enhance the accuracy and
Recalibrating disease parameters for increasing realism in modeling epidemics in closed settings.
Bioglio, Livio; Génois, Mathieu; Vestergaard, Christian L; Poletto, Chiara; Barrat, Alain; Colizza, Vittoria
2016-11-14
The homogeneous mixing assumption is widely adopted in epidemic modelling for its parsimony and represents the building block of more complex approaches, including very detailed agent-based models. The latter assume homogeneous mixing within schools, workplaces and households, mostly for the lack of detailed information on human contact behaviour within these settings. The recent data availability on high-resolution face-to-face interactions makes it now possible to assess the goodness of this simplified scheme in reproducing relevant aspects of the infection dynamics. We consider empirical contact networks gathered in different contexts, as well as synthetic data obtained through realistic models of contacts in structured populations. We perform stochastic spreading simulations on these contact networks and in populations of the same size under a homogeneous mixing hypothesis. We adjust the epidemiological parameters of the latter in order to fit the prevalence curve of the contact epidemic model. We quantify the agreement by comparing epidemic peak times, peak values, and epidemic sizes. Good approximations of the peak times and peak values are obtained with the homogeneous mixing approach, with a median relative difference smaller than 20 % in all cases investigated. Accuracy in reproducing the peak time depends on the setting under study, while for the peak value it is independent of the setting. Recalibration is found to be linear in the epidemic parameters used in the contact data simulations, showing changes across empirical settings but robustness across groups and population sizes. An adequate rescaling of the epidemiological parameters can yield a good agreement between the epidemic curves obtained with a real contact network and a homogeneous mixing approach in a population of the same size. The use of such recalibrated homogeneous mixing approximations would enhance the accuracy and realism of agent-based simulations and limit the intrinsic biases of
The threshold of a stochastic SIQS epidemic model
Zhang, Xiao-Bing; Huo, Hai-Feng; Xiang, Hong; Shi, Qihong; Li, Dungang
2017-09-01
In this paper, we present the threshold of a stochastic SIQS epidemic model which determines the extinction and persistence of the disease. Furthermore, we find that noise can suppress the disease outbreak. Numerical simulations are also carried out to confirm the analytical results.
A final size relation for epidemic models of vector-transmitted diseases
Fred Brauer
2017-01-01
We formulate and analyze an age of infection model for epidemics of diseases transmitted by a vector, including the possibility of direct transmission as well. We show how to determine a basic reproduction number. While there is no explicit final size relation as for diseases transmitted directly, we are able to obtain estimates for the final size of the epidemic.
International Nuclear Information System (INIS)
Meng Xinzhu; Jiao Jianjun; Chen Lansun
2009-01-01
Since the investigation of impulsive delay differential equations is beginning, the literature on delay epidemic models with pulse vaccination is not extensive. In this paper, we propose a new SEIRS epidemic disease model with two profitless delays and vertical transmission, and analyze the dynamics behaviors of the model under pulse vaccination. Using the discrete dynamical system determined by the stroboscopic map, we obtain a 'infection-free' periodic solution, further, show that the 'infection-free' periodic solution is globally attractive when some parameters of the model are under appropriate conditions. Using a new modeling method, we obtain sufficient condition for the permanence of the epidemic model with pulse vaccination. We show that time delays, pulse vaccination and vertical transmission can bring different effects on the dynamics behaviors of the model by numerical analysis. Our results also show the delays are 'profitless'. In this paper, the main feature is to introduce two discrete time delays, vertical transmission and impulse into SEIRS epidemic model and to give pulse vaccination strategies.
International Nuclear Information System (INIS)
Li Ke-Zan; Xu Zhong-Pu; Zhu Guang-Hu; Ding Yong
2014-01-01
Recent research results indicate that individual awareness can play an important influence on epidemic spreading in networks. By local stability analysis, a significant conclusion is that the embedded awareness in an epidemic network can increase its epidemic threshold. In this paper, by using limit theory and dynamical system theory, we further give global stability analysis of a susceptible-infected-susceptible (SIS) epidemic model on networks with awareness. Results show that the obtained epidemic threshold is also a global stability condition for its endemic equilibrium, which implies the embedded awareness can enhance the epidemic threshold globally. Some numerical examples are presented to verify the theoretical results. (interdisciplinary physics and related areas of science and technology)
Halting HIV/AIDS with avatars and havatars: a virtual world approach to modelling epidemics
Directory of Open Access Journals (Sweden)
Smith? Robert J
2009-11-01
Full Text Available Abstract Background A major deficit of all approaches to epidemic modelling to date has been the need to approximate or guess at human behaviour in disease-transmission-related contexts. Avatars are generally human-like figures in virtual computer worlds controlled by human individuals. Methods We introduce the concept of a "havatar", which is a (human, avatar pairing. Evidence is mounting that this pairing behaves in virtual contexts much like the human in the pairing might behave in analogous real-world contexts. Results We propose that studies of havatars, in a virtual world, may give a realistic approximation of human behaviour in real-world contexts. If the virtual world approximates the real world in relevant details (geography, transportation, etc., virtual epidemics in that world could accurately simulate real-world epidemics. Havatar modelling of epidemics therefore offers a complementary tool for tackling how best to halt epidemics, including perhaps HIV/AIDS, since sexual behaviour is a significant component of some virtual worlds, such as Second Life. Conclusion Havatars place the control parameters of an epidemic in the hands of each individual. By providing tools that everyone can understand and use, we could democratise epidemiology.
Travelling wave solutions for an infection-age structured epidemic model with external supplies
International Nuclear Information System (INIS)
Ducrot, Arnaud; Magal, Pierre
2011-01-01
The aim of this paper is to investigate the spatial invasion of some infectious disease. The contamination process is described by the age since infection. Compared with the classical Kermack and McKendrick's model, the vital dynamic is not omitted, and we allow some constant input flux into the population. This problem is rather natural in the context of epidemic problems and it has not been studied. Here we prove an existence and non-existence result for travelling wave solutions. We also describe the minimal wave speed. We are able to construct a suitable Lyapunov like functional decreasing along the travelling wave allowing to derive some qualitative properties, namely their convergence towards equilibrium points at x = ±∞
Heroin epidemics, treatment and ODE modelling.
White, Emma; Comiskey, Catherine
2007-07-01
The UN [United Nations Office on Drugs and Crime (UNODC): World Drug Report, 2005, vol. 1: Analysis. UNODC, 2005.], EU [European Monitoring Centre for Drugs and Drug Addiction (EMCDDA): Annual Report, 2005.http://annualreport.emcdda.eu.int/en/home-en.html.] and WHO [World Health Organisation (WHO): Biregional Strategy for Harm Reduction, 2005-2009. HIV and Injecting Drug Use. WHO, 2005.] have consistently highlighted in recent years the ongoing and persistent nature of opiate and particularly heroin use on a global scale. While this is a global phenomenon, authors have emphasised the significant impact such an epidemic has on individual lives and on society. National prevalence studies have indicated the scale of the problem, but the drug-using career, typically consisting of initiation, habitual use, a treatment-relapse cycle and eventual recovery, is not well understood. This paper presents one of the first ODE models of opiate addiction, based on the principles of mathematical epidemiology. The aim of this model is to identify parameters of interest for further study, with a view to informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness. An epidemic threshold value, R(0), is proposed for the drug-using career. Sensitivity analysis is performed on R(0) and it is then used to examine the stability of the system. A condition under which a backward bifurcation may exist is found, as are conditions that permit the existence of one or more endemic equilibria. A key result arising from this model is that prevention is indeed better than cure.
Hop-by-HopWorm Propagation with Carryover Epidemic Model in Mobile Sensor Networks
Directory of Open Access Journals (Sweden)
Jun-Won Ho
2015-10-01
Full Text Available In the internet, a worm is usually propagated in a random multi-hop contact manner. However, the attacker will not likely select this random multi-hop propagation approach in a mobile sensor network. This is because multi-hop worm route paths to random vulnerable targets can be often breached due to node mobility, leading to failure of fast worm spread under this strategy. Therefore, an appropriate propagation strategy is needed for mobile sensor worms. To meet this need, we discuss a hop-by-hop worm propagation model in mobile sensor networks. In a hop-by-hop worm propagation model, benign nodes are infected by worm in neighbor-to-neighbor spread manner. Since worm infection occurs in hop-by-hop contact, it is not substantially affected by a route breach incurred by node mobility. We also propose the carryover epidemic model to deal with the worm infection quota deficiency that might occur when employing an epidemic model in a mobile sensor network. We analyze worm infection capability under the carryover epidemic model. Moreover, we simulate hop-by-hop worm propagation with carryover epidemic model by using an ns-2 simulator. The simulation results demonstrate that infection quota carryovers are seldom observed where a node’s maximum speed is no less than 20 m/s.
A chaotic model for the epidemic of Ebola virus disease in West Africa (2013-2016)
Mangiarotti, Sylvain; Peyre, Marisa; Huc, Mireille
2016-11-01
An epidemic of Ebola Virus Disease (EVD) broke out in Guinea in December 2013. It was only identified in March 2014 while it had already spread out in Liberia and Sierra Leone. The spill over of the disease became uncontrollable and the epidemic could not be stopped before 2016. The time evolution of this epidemic is revisited here with the global modeling technique which was designed to obtain the deterministic models from single time series. A generalized formulation of this technique for multivariate time series is introduced. It is applied to the epidemic of EVD in West Africa focusing on the period between March 2014 and January 2015, that is, before any detected signs of weakening. Data gathered by the World Health Organization, based on the official publications of the Ministries of Health of the three main countries involved in this epidemic, are considered in our analysis. Two observed time series are used: the daily numbers of infections and deaths. A four-dimensional model producing a very complex dynamical behavior is obtained. The model is tested in order to investigate its skills and drawbacks. Our global analysis clearly helps to distinguish three main stages during the epidemic. A characterization of the obtained attractor is also performed. In particular, the topology of the chaotic attractor is analyzed and a skeleton is obtained for its structure.
Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects.
Baumann, Hendrik; Sandmann, Werner
2016-01-01
Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.
Epidemic classification of phytosanitary situations on cereal crops using mathematical modeling
Most plant protection researchers and experts divide emerging phytosanitary situations into three classes: epidemic, moderate development of disease, and yield depression. The known principles and methods for estimating these situations (Van der Plank J.E., Kranz J. et al.) do not fully describe th...
International Nuclear Information System (INIS)
Lu, Yunfan; Wang, Jun; Niu, Hongli
2015-01-01
An agent-based financial stock price model is developed and investigated by a stochastic interacting epidemic system, which is one of the statistical physics systems and has been used to model the spread of an epidemic or a forest fire. Numerical and statistical analysis are performed on the simulated returns of the proposed financial model. Complexity properties of the financial time series are explored by calculating the correlation dimension and using the modified multiscale entropy method. In order to verify the rationality of the financial model, the real stock market indexes, Shanghai Composite Index and Shenzhen Component Index, are studied in comparison with the simulation data of the proposed model for the different infectiousness parameters. The empirical research reveals that this financial model can reproduce some important features of the real stock markets. - Highlights: • A new agent-based financial price model is developed by stochastic interacting epidemic system. • The structure of the proposed model allows to simulate the financial dynamics. • Correlation dimension and MMSE are applied to complexity analysis of financial time series. • Empirical results show the rationality of the proposed financial model
Energy Technology Data Exchange (ETDEWEB)
Lu, Yunfan, E-mail: yunfanlu@yeah.net; Wang, Jun; Niu, Hongli
2015-06-12
An agent-based financial stock price model is developed and investigated by a stochastic interacting epidemic system, which is one of the statistical physics systems and has been used to model the spread of an epidemic or a forest fire. Numerical and statistical analysis are performed on the simulated returns of the proposed financial model. Complexity properties of the financial time series are explored by calculating the correlation dimension and using the modified multiscale entropy method. In order to verify the rationality of the financial model, the real stock market indexes, Shanghai Composite Index and Shenzhen Component Index, are studied in comparison with the simulation data of the proposed model for the different infectiousness parameters. The empirical research reveals that this financial model can reproduce some important features of the real stock markets. - Highlights: • A new agent-based financial price model is developed by stochastic interacting epidemic system. • The structure of the proposed model allows to simulate the financial dynamics. • Correlation dimension and MMSE are applied to complexity analysis of financial time series. • Empirical results show the rationality of the proposed financial model.
Epidemics spread in heterogeneous populations
Capała, Karol; Dybiec, Bartłomiej
2017-05-01
Individuals building populations are subject to variability. This variability affects progress of epidemic outbreaks, because individuals tend to be more or less resistant. Individuals also differ with respect to their recovery rate. Here, properties of the SIR model in inhomogeneous populations are studied. It is shown that a small change in model's parameters, e.g. recovery or infection rate, can substantially change properties of final states which is especially well-visible in distributions of the epidemic size. In addition to the epidemic size and radii distributions, the paper explores first passage time properties of epidemic outbreaks.
Low dimensional chaotic models for the plague epidemic in Bombay (1896–1911)
International Nuclear Information System (INIS)
Mangiarotti, Sylvain
2015-01-01
A plague epidemic broke out in Bombay in 1896 and became endemic. From 1905 to 1911, the epidemic was closely monitored by an Advisory Committee appointed to investigate the causes of the disease in any way. An impressive quantity of information was gathered, analyzed and published. Published data include records of the number of people who died from plague, and of the two main populations of rodents which were infected by plague in Bombay city. In the present paper, these data are revisited using a global modeling technique. This technique is applied to both single and multivariate observational time series. Several models are obtained for which a chaotic behavior can be observed. Obtaining such models proves that the dynamics of plague can be approximated by low-dimensional deterministic systems that can produce chaos. The multivariate models give a strong argument for interactive couplings between the epidemic and the epizootics of the two main species of rat. An interpretation of this coupling is given.
Epidemics in adaptive networks with community structure
Shaw, Leah; Tunc, Ilker
2010-03-01
Models for epidemic spread on static social networks do not account for changes in individuals' social interactions. Recent studies of adaptive networks have modeled avoidance behavior, as non-infected individuals try to avoid contact with infectives. Such models have not generally included realistic social structure. Here we study epidemic spread on an adaptive network with community structure. We model the effect of heterogeneous communities on infection levels and epidemic extinction. We also show how an epidemic can alter the community structure.
Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects.
Directory of Open Access Journals (Sweden)
Hendrik Baumann
Full Text Available Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.
epiDMS: Data Management and Analytics for Decision-Making From Epidemic Spread Simulation Ensembles.
Liu, Sicong; Poccia, Silvestro; Candan, K Selçuk; Chowell, Gerardo; Sapino, Maria Luisa
2016-12-01
Carefully calibrated large-scale computational models of epidemic spread represent a powerful tool to support the decision-making process during epidemic emergencies. Epidemic models are being increasingly used for generating forecasts of the spatial-temporal progression of epidemics at different spatial scales and for assessing the likely impact of different intervention strategies. However, the management and analysis of simulation ensembles stemming from large-scale computational models pose challenges, particularly when dealing with multiple interdependent parameters, spanning multiple layers and geospatial frames, affected by complex dynamic processes operating at different resolutions. We describe and illustrate with examples a novel epidemic simulation data management system, epiDMS, that was developed to address the challenges that arise from the need to generate, search, visualize, and analyze, in a scalable manner, large volumes of epidemic simulation ensembles and observations during the progression of an epidemic. epiDMS is a publicly available system that facilitates management and analysis of large epidemic simulation ensembles. epiDMS aims to fill an important hole in decision-making during healthcare emergencies by enabling critical services with significant economic and health impact. © The Author 2016. Published by Oxford University Press for the Infectious Diseases Society of America. All rights reserved. For permissions, e-mail journals.permissions@oup.com.
Rainfall mediations in the spreading of epidemic cholera
Righetto, L.; Bertuzzo, E.; Mari, L.; Schild, E.; Casagrandi, R.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.
2013-10-01
Following the empirical evidence of a clear correlation between rainfall events and cholera resurgence that was observed in particular during the recent outbreak in Haiti, a spatially explicit model of epidemic cholera is re-examined. Specifically, we test a multivariate Poisson rainfall generator, with parameters varying in space and time, as a driver of enhanced disease transmission. The relevance of the issue relates to the key insight that predictive mathematical models may provide into the course of an ongoing cholera epidemic aiding emergency management (say, in allocating life-saving supplies or health care staff) or in evaluating alternative management strategies. Our model consists of a set of dynamical equations (SIRB-like i.e. subdivided into the compartments of Susceptible, Infected and Recovered individuals, and including a balance of Bacterial concentrations in the water reservoir) describing a connected network of human communities where the infection results from the exposure to excess concentrations of pathogens in the water. These, in turn, are driven by rainfall washout of open-air defecation sites or cesspool overflows, hydrologic transport through waterways and by mobility of susceptible and infected individuals. We perform an a posteriori analysis (from the beginning of the epidemic in October 2010 until December 2011) to test the model reliability in predicting cholera cases and in testing control measures, involving vaccination and sanitation campaigns, for the ongoing epidemic. Even though predicting reliably the timing of the epidemic resurgence proves difficult due to rainfall inter-annual variability, we find that the model can reasonably quantify the total number of reported infection cases in the selected time-span. We then run a multi-seasonal prediction of the course of the epidemic until December 2015, to investigate conditions for further resurgences and endemicity of cholera in the region with a view to policies which may bring to
On the modeling of epidemics under the influence of risk perception
De Lillo, S.; Fioriti, G.; Prioriello, M.L.
2017-01-01
An epidemic spreading model is presented in the framework of the kinetic theory of active particles. The model is characterized by the influence of risk perception which can reduce the diffusion of infection. The evolution of the system is modeled through nonlinear interactions, whose output is
Impact of delay on disease outbreak in a spatial epidemic model
Zhao, Xia-Xia; Wang, Jian-Zhong
2015-04-01
One of the central issues in studying epidemic spreading is the mechanism on disease outbreak. In this paper, we investigate the effects of time delay on disease outbreak in spatial epidemics based on a reaction-diffusion model. By mathematical analysis and numerical simulations, we show that when time delay is more than a critical value, the disease outbreaks. The obtained results show that the time delay is an important factor in the spread of the disease, which may provide new insights on disease control.
Epidemic Processes on Complex Networks : Modelling, Simulation and Algorithms
Van de Bovenkamp, R.
2015-01-01
Local interactions on a graph will lead to global dynamic behaviour. In this thesis we focus on two types of dynamic processes on graphs: the Susceptible-Infected-Susceptilbe (SIS) virus spreading model, and gossip style epidemic algorithms. The largest part of this thesis is devoted to the SIS
Ackley, SF; Liu, F; Porco, TC; Pepperell, CS
2015-01-01
© 2015 Ackley et al. Late 19th century epidemics of tuberculosis (TB) inWestern Canadian First Nations resulted in peak TB mortality rates more than six times the highest rates recorded in Europe. Using a mathematical modeling approach and historical TB mortality time series, we investigate potential causes of high TB mortality and rapid epidemic decline in First Nations from 1885 to 1940. We explore two potential causes of dramatic epidemic dynamics observed in this setting: first, we explor...
Human Mobility Patterns and Cholera Epidemics: a Spatially Explicit Modeling Approach
Mari, L.; Bertuzzo, E.; Righetto, L.; Casagrandi, R.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.
2010-12-01
Cholera is an acute enteric disease caused by the ingestion of water or food contaminated by the bacterium Vibrio cholerae. Although most infected individuals do not develop severe symptoms, their stool may contain huge quantities of V.~cholerae cells. Therefore, while traveling or commuting, asymptomatic carriers can be responsible for the long-range dissemination of the disease. As a consequence, human mobility is an alternative and efficient driver for the spread of cholera, whose primary propagation pathway is hydrological transport through river networks. We present a multi-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of V.~cholerae due to human movement. In particular, building on top of state-of-the-art spatially explicit models for cholera spread through surface waters, we describe human movement and its effects on the propagation of the disease by means of a gravity-model approach borrowed from transportation theory. Gravity-like contact processes have been widely used in epidemiology, because they can satisfactorily depict human movement when data on actual mobility patterns are not available. We test our model against epidemiological data recorded during the cholera outbreak occurred in the KwaZulu-Natal province of South Africa during years 2000--2001. We show that human mobility does actually play an important role in the formation of the spatiotemporal patterns of cholera epidemics. In particular, long-range human movement may determine inter-catchment dissemination of V.~cholerae cells, thus in turn explaining the emergence of epidemic patterns that cannot be produced by hydrological transport alone. We also show that particular attention has to be devoted to study how heterogeneously distributed drinking water supplies and sanitation conditions may affect cholera transmission.
Epidemic spreading on contact networks with adaptive weights.
Zhu, Guanghu; Chen, Guanrong; Xu, Xin-Jian; Fu, Xinchu
2013-01-21
The heterogeneous patterns of interactions within a population are often described by contact networks, but the variety and adaptivity of contact strengths are usually ignored. This paper proposes a modified epidemic SIS model with a birth-death process and nonlinear infectivity on an adaptive and weighted contact network. The links' weights, named as 'adaptive weights', which indicate the intimacy or familiarity between two connected individuals, will reduce as the disease develops. Through mathematical and numerical analyses, conditions are established for population extermination, disease extinction and infection persistence. Particularly, it is found that the fixed weights setting can trigger the epidemic incidence, and that the adaptivity of weights cannot change the epidemic threshold but it can accelerate the disease decay and lower the endemic level. Finally, some corresponding control measures are suggested. Copyright © 2012 Elsevier Ltd. All rights reserved.
Dynamic complexities in a seasonal prevention epidemic model with birth pulses
International Nuclear Information System (INIS)
Gao Shujing; Chen Lansun; Sun Lihua
2005-01-01
In most of population dynamics, increases in population due to birth are assumed to be time-dependent, but many species reproduce only during a single period of the year. In this paper, we propose an epidemic model with density-dependent birth pulses and seasonal prevention. Using the discrete dynamical system determined by stroboscopic map, we obtain the local or global stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behaviors of the epidemic model with birth pulses and seasonal prevention are very complex, including small amplitude oscillations, large-amplitude multi-annual cycles and chaos. This suggests that birth pulse, in effect, provides a natural period or cyclicity that may lead a period-doubling route to chaos
Epidemics in interconnected small-world networks
Liu, M.; Li, D.; Qin, P.; Liu, C.; Wang, H.; Wang, F.
2015-01-01
Networks can be used to describe the interconnections among individuals, which play an important role in the spread of disease. Although the small-world effect has been found to have a significant impact on epidemics in single networks, the small-world effect on epidemics in interconnected networks
Trajanovski, Stojan; Guo, Dongchao; Van Mieghem, Piet
2015-09-01
The continuous-time adaptive susceptible-infected-susceptible (ASIS) epidemic model and the adaptive information diffusion (AID) model are two adaptive spreading processes on networks, in which a link in the network changes depending on the infectious state of its end nodes, but in opposite ways: (i) In the ASIS model a link is removed between two nodes if exactly one of the nodes is infected to suppress the epidemic, while a link is created in the AID model to speed up the information diffusion; (ii) a link is created between two susceptible nodes in the ASIS model to strengthen the healthy part of the network, while a link is broken in the AID model due to the lack of interest in informationless nodes. The ASIS and AID models may be considered as first-order models for cascades in real-world networks. While the ASIS model has been exploited in the literature, we show that the AID model is realistic by obtaining a good fit with Facebook data. Contrary to the common belief and intuition for such similar models, we show that the ASIS and AID models exhibit different but not opposite properties. Most remarkably, a unique metastable state always exists in the ASIS model, while there an hourglass-shaped region of instability in the AID model. Moreover, the epidemic threshold is a linear function in the effective link-breaking rate in the AID model, while it is almost constant but noisy in the AID model.
An online spatiotemporal prediction model for dengue fever epidemic in Kaohsiung (Taiwan).
Yu, Hwa-Lung; Angulo, José M; Cheng, Ming-Hung; Wu, Jiaping; Christakos, George
2014-05-01
The emergence and re-emergence of disease epidemics is a complex question that may be influenced by diverse factors, including the space-time dynamics of human populations, environmental conditions, and associated uncertainties. This study proposes a stochastic framework to integrate space-time dynamics in the form of a Susceptible-Infected-Recovered (SIR) model, together with uncertain disease observations, into a Bayesian maximum entropy (BME) framework. The resulting model (BME-SIR) can be used to predict space-time disease spread. Specifically, it was applied to obtain a space-time prediction of the dengue fever (DF) epidemic that took place in Kaohsiung City (Taiwan) during 2002. In implementing the model, the SIR parameters were continually updated and information on new cases of infection was incorporated. The results obtained show that the proposed model is rigorous to user-specified initial values of unknown model parameters, that is, transmission and recovery rates. In general, this model provides a good characterization of the spatial diffusion of the DF epidemic, especially in the city districts proximal to the location of the outbreak. Prediction performance may be affected by various factors, such as virus serotypes and human intervention, which can change the space-time dynamics of disease diffusion. The proposed BME-SIR disease prediction model can provide government agencies with a valuable reference for the timely identification, control, and prevention of DF spread in space and time. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
A stochastic SIS epidemic model with vaccination
Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming
2017-11-01
In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R0s > 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.
Rabies epidemic model with uncertainty in parameters: crisp and fuzzy approaches
Ndii, M. Z.; Amarti, Z.; Wiraningsih, E. D.; Supriatna, A. K.
2018-03-01
A deterministic mathematical model is formulated to investigate the transmission dynamics of rabies. In particular, we investigate the effects of vaccination, carrying capacity and the transmission rate on the rabies epidemics and allow for uncertainty in the parameters. We perform crisp and fuzzy approaches. We find that, in the case of crisp parameters, rabies epidemics may be interrupted when the carrying capacity and the transmission rate are not high. Our findings suggest that limiting the growth of dog population and reducing the potential contact between susceptible and infectious dogs may aid in interrupting rabies epidemics. We extend the work by considering a fuzzy carrying capacity and allow for low, medium, and high level of carrying capacity. The result confirms the results obtained by using crisp carrying capacity, that is, when the carrying capacity is not too high, the vaccination could confine the disease effectively.
Epidemic spreading in time-varying community networks.
Ren, Guangming; Wang, Xingyuan
2014-06-01
The spreading processes of many infectious diseases have comparable time scale as the network evolution. Here, we present a simple networks model with time-varying community structure, and investigate susceptible-infected-susceptible epidemic spreading processes in this model. By both theoretic analysis and numerical simulations, we show that the efficiency of epidemic spreading in this model depends intensively on the mobility rate q of the individuals among communities. We also find that there exists a mobility rate threshold qc. The epidemic will survive when q > qc and die when q epidemic spreading in complex networks with community structure.
The effects of global awareness on the spreading of epidemics in multiplex networks
Zang, Haijuan
2018-02-01
It is increasingly recognized that understanding the complex interplay patterns between epidemic spreading and human behavioral is a key component of successful infection control efforts. In particular, individuals can obtain the information about epidemics and respond by altering their behaviors, which can affect the spreading dynamics as well. Besides, because the existence of herd-like behaviors, individuals are very easy to be influenced by the global awareness information. Here, in this paper, we propose a global awareness controlled spreading model (GACS) to explore the interplay between the coupled dynamical processes. Using the global microscopic Markov chain approach, we obtain the analytical results for the epidemic thresholds, which shows a high accuracy by comparison with lots of Monte Carlo simulations. Furthermore, considering other classical models used to describe the coupled dynamical processes, including the local awareness controlled contagion spreading (LACS) model, Susceptible-Infected-Susceptible-Unaware-Aware-Unaware (SIS-UAU) model and the single layer occasion, we make a detailed comparisons between the GACS with them. Although the comparisons and results depend on the parameters each model has, the GACS model always shows a strong restrain effects on epidemic spreading process. Our results give us a better understanding of the coupled dynamical processes and highlights the importance of considering the spreading of global awareness in the control of epidemics.
Spatially explicit modelling of cholera epidemics
Finger, F.; Bertuzzo, E.; Mari, L.; Knox, A. C.; Gatto, M.; Rinaldo, A.
2013-12-01
Epidemiological models can provide crucial understanding about the dynamics of infectious diseases. Possible applications range from real-time forecasting and allocation of health care resources to testing alternative intervention mechanisms such as vaccines, antibiotics or the improvement of sanitary conditions. We apply a spatially explicit model to the cholera epidemic that struck Haiti in October 2010 and is still ongoing. The dynamics of susceptibles as well as symptomatic and asymptomatic infectives are modelled at the scale of local human communities. Dissemination of Vibrio cholerae through hydrological transport and human mobility along the road network is explicitly taken into account, as well as the effect of rainfall as a driver of increasing disease incidence. The model is calibrated using a dataset of reported cholera cases. We further model the long term impact of several types of interventions on the disease dynamics by varying parameters appropriately. Key epidemiological mechanisms and parameters which affect the efficiency of treatments such as antibiotics are identified. Our results lead to conclusions about the influence of different intervention strategies on the overall epidemiological dynamics.
The origin and emergence of an HIV-1 epidemic:
DEFF Research Database (Denmark)
Bruhn, Christian Anders Wathne; Audelin, Anne M.; Helleberg, Marie
2014-01-01
To describe, at patient-level detail, the determining events and factors involved in the development of a country's HIV-1 epidemic.......To describe, at patient-level detail, the determining events and factors involved in the development of a country's HIV-1 epidemic....
Directory of Open Access Journals (Sweden)
Sarah F. Ackley
2015-09-01
Full Text Available Late 19th century epidemics of tuberculosis (TB in Western Canadian First Nations resulted in peak TB mortality rates more than six times the highest rates recorded in Europe. Using a mathematical modeling approach and historical TB mortality time series, we investigate potential causes of high TB mortality and rapid epidemic decline in First Nations from 1885 to 1940. We explore two potential causes of dramatic epidemic dynamics observed in this setting: first, we explore effects of famine prior to 1900 on both TB and population dynamics. Malnutrition is recognized as an individual-level risk factor for TB progression and mortality; its population-level effects on TB epidemics have not been explored previously. Second, we explore effects of heterogeneity in susceptibility to TB in two ways: modeling heterogeneity in susceptibility to infection, and heterogeneity in risk of developing disease once infected. Our results indicate that models lacking famine-related changes in TB parameters or heterogeneity result in an implausibly poor fit to both the TB mortality time series and census data; the inclusion of these features allows for the characteristic decline and rise in population observed in First Nations during this time period and confers improved fits to TB mortality data.
Epidemics spreading in interconnected complex networks
International Nuclear Information System (INIS)
Wang, Y.; Xiao, G.
2012-01-01
We study epidemic spreading in two interconnected complex networks. It is found that in our model the epidemic threshold of the interconnected network is always lower than that in any of the two component networks. Detailed theoretical analysis is proposed which allows quick and accurate calculations of epidemic threshold and average outbreak/epidemic size. Theoretical analysis and simulation results show that, generally speaking, the epidemic size is not significantly affected by the inter-network correlation. In interdependent networks which can be viewed as a special case of interconnected networks, however, impacts of inter-network correlation on the epidemic threshold and outbreak size are more significant. -- Highlights: ► We study epidemic spreading in two interconnected complex networks. ► The epidemic threshold is lower than that in any of the two networks. And Interconnection correlation has impacts on threshold and average outbreak size. ► Detailed theoretical analysis is proposed which allows quick and accurate calculations of epidemic threshold and average outbreak/epidemic size. ► We demonstrated and proved that Interconnection correlation does not affect epidemic size significantly. ► In interdependent networks, impacts of inter-network correlation on the epidemic threshold and outbreak size are more significant.
Epidemics spreading in interconnected complex networks
Energy Technology Data Exchange (ETDEWEB)
Wang, Y. [School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (Singapore); Institute of High Performance Computing, Agency for Science, Technology and Research (A-STAR), Singapore 138632 (Singapore); Xiao, G., E-mail: egxxiao@ntu.edu.sg [School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (Singapore)
2012-09-03
We study epidemic spreading in two interconnected complex networks. It is found that in our model the epidemic threshold of the interconnected network is always lower than that in any of the two component networks. Detailed theoretical analysis is proposed which allows quick and accurate calculations of epidemic threshold and average outbreak/epidemic size. Theoretical analysis and simulation results show that, generally speaking, the epidemic size is not significantly affected by the inter-network correlation. In interdependent networks which can be viewed as a special case of interconnected networks, however, impacts of inter-network correlation on the epidemic threshold and outbreak size are more significant. -- Highlights: ► We study epidemic spreading in two interconnected complex networks. ► The epidemic threshold is lower than that in any of the two networks. And Interconnection correlation has impacts on threshold and average outbreak size. ► Detailed theoretical analysis is proposed which allows quick and accurate calculations of epidemic threshold and average outbreak/epidemic size. ► We demonstrated and proved that Interconnection correlation does not affect epidemic size significantly. ► In interdependent networks, impacts of inter-network correlation on the epidemic threshold and outbreak size are more significant.
Mathematical modeling, analysis and Markov Chain Monte Carlo simulation of Ebola epidemics
Tulu, Thomas Wetere; Tian, Boping; Wu, Zunyou
Ebola virus infection is a severe infectious disease with the highest case fatality rate which become the global public health treat now. What makes the disease the worst of all is no specific effective treatment available, its dynamics is not much researched and understood. In this article a new mathematical model incorporating both vaccination and quarantine to study the dynamics of Ebola epidemic has been developed and comprehensively analyzed. The existence as well as uniqueness of the solution to the model is also verified and the basic reproduction number is calculated. Besides, stability conditions are also checked and finally simulation is done using both Euler method and one of the top ten most influential algorithm known as Markov Chain Monte Carlo (MCMC) method. Different rates of vaccination to predict the effect of vaccination on the infected individual over time and that of quarantine are discussed. The results show that quarantine and vaccination are very effective ways to control Ebola epidemic. From our study it was also seen that there is less possibility of an individual for getting Ebola virus for the second time if they survived his/her first infection. Last but not least real data has been fitted to the model, showing that it can used to predict the dynamic of Ebola epidemic.
Epidemic processes in complex networks
Pastor-Satorras, Romualdo; Castellano, Claudio; Van Mieghem, Piet; Vespignani, Alessandro
2015-07-01
In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.
Perspectives on model forecasts of the 2014-2015 Ebola epidemic in West Africa
DEFF Research Database (Denmark)
Chowell, Gerardo; Viboud, Cécile; Simonsen, Lone
2017-01-01
The unprecedented impact and modeling efforts associated with the 2014–2015 Ebola epidemic in West Africa provides a unique opportunity to document the performances and caveats of forecasting approaches used in near-real time for generating evidence and to guide policy. A number of international...... academic groups have developed and parameterized mathematical models of disease spread to forecast the trajectory of the outbreak. These modeling efforts often relied on limited epidemiological data to derive key transmission and severity parameters, which are needed to calibrate mechanistic models. Here...... changes and case clustering; (3) challenges in forecasting the long-term epidemic impact very early in the outbreak; and (4) ways to move forward. We conclude that rapid availability of aggregated population-level data and detailed information on a subset of transmission chains is crucial to characterize...
Epidemic spreading in time-varying community networks
Energy Technology Data Exchange (ETDEWEB)
Ren, Guangming, E-mail: wangxy@dlut.edu.cn, E-mail: ren-guang-ming@163.com [School of Electronic and Information, Guangdong Polytechnic Normal University, Guangzhou 510665 (China); Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024 (China); Wang, Xingyuan, E-mail: wangxy@dlut.edu.cn, E-mail: ren-guang-ming@163.com [Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024 (China)
2014-06-15
The spreading processes of many infectious diseases have comparable time scale as the network evolution. Here, we present a simple networks model with time-varying community structure, and investigate susceptible-infected-susceptible epidemic spreading processes in this model. By both theoretic analysis and numerical simulations, we show that the efficiency of epidemic spreading in this model depends intensively on the mobility rate q of the individuals among communities. We also find that there exists a mobility rate threshold q{sub c}. The epidemic will survive when q > q{sub c} and die when q < q{sub c}. These results can help understanding the impacts of human travel on the epidemic spreading in complex networks with community structure.
Epidemic spreading in time-varying community networks
International Nuclear Information System (INIS)
Ren, Guangming; Wang, Xingyuan
2014-01-01
The spreading processes of many infectious diseases have comparable time scale as the network evolution. Here, we present a simple networks model with time-varying community structure, and investigate susceptible-infected-susceptible epidemic spreading processes in this model. By both theoretic analysis and numerical simulations, we show that the efficiency of epidemic spreading in this model depends intensively on the mobility rate q of the individuals among communities. We also find that there exists a mobility rate threshold q c . The epidemic will survive when q > q c and die when q c . These results can help understanding the impacts of human travel on the epidemic spreading in complex networks with community structure
The Importance of Being Hybrid for Spatial Epidemic Models:A Multi-Scale Approach
Directory of Open Access Journals (Sweden)
Arnaud Banos
2015-11-01
Full Text Available This work addresses the spread of a disease within an urban system, deﬁnedas a network of interconnected cities. The ﬁrst step consists of comparing two differentapproaches: a macroscopic one, based on a system of coupled Ordinary DifferentialEquations (ODE Susceptible-Infected-Recovered (SIR systems exploiting populations onnodes and ﬂows on edges (so-called metapopulational model, and a hybrid one, couplingODE SIR systems on nodes and agents traveling on edges. Under homogeneous conditions(mean ﬁeld approximation, this comparison leads to similar results on the outputs on whichwe focus (the maximum intensity of the epidemic, its duration and the time of the epidemicpeak. However, when it comes to setting up epidemic control strategies, results rapidlydiverge between the two approaches, and it appears that the full macroscopic model is notcompletely adapted to these questions. In this paper, we focus on some control strategies,which are quarantine, avoidance and risk culture, to explore the differences, advantages anddisadvantages of the two models and discuss the importance of being hybrid when modelingand simulating epidemic spread at the level of a whole urban system.
Global dynamics of a dengue epidemic mathematical model
International Nuclear Information System (INIS)
Cai Liming; Guo Shumin; Li, XueZhi; Ghosh, Mini
2009-01-01
The paper investigates the global stability of a dengue epidemic model with saturation and bilinear incidence. The constant human recruitment rate and exponential natural death, as well as vector population with asymptotically constant population, are incorporated into the model. The model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. The stability of these two equilibria is controlled by the threshold number R 0 . It is shown that if R 0 is less than one, the disease-free equilibrium is globally asymptotically stable and in such a case the endemic equilibrium does not exist; if R 0 is greater than one, then the disease persists and the unique endemic equilibrium is globally asymptotically stable.
Multiple routes transmitted epidemics on multiplex networks
International Nuclear Information System (INIS)
Zhao, Dawei; Li, Lixiang; Peng, Haipeng; Luo, Qun; Yang, Yixian
2014-01-01
This letter investigates the multiple routes transmitted epidemic process on multiplex networks. We propose detailed theoretical analysis that allows us to accurately calculate the epidemic threshold and outbreak size. It is found that the epidemic can spread across the multiplex network even if all the network layers are well below their respective epidemic thresholds. Strong positive degree–degree correlation of nodes in multiplex network could lead to a much lower epidemic threshold and a relatively smaller outbreak size. However, the average similarity of neighbors from different layers of nodes has no obvious effect on the epidemic threshold and outbreak size. -- Highlights: •We studies multiple routes transmitted epidemic process on multiplex networks. •SIR model and bond percolation theory are used to analyze the epidemic processes. •We derive equations to accurately calculate the epidemic threshold and outbreak size. •ASN has no effect on the epidemic threshold and outbreak size. •Strong positive DDC leads to a lower epidemic threshold and a smaller outbreak size.
Multiple routes transmitted epidemics on multiplex networks
Energy Technology Data Exchange (ETDEWEB)
Zhao, Dawei [Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, P.O. Box 145, Beijing 100876 (China); National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Shandong Provincial Key Laboratory of Computer Network, Shandong Computer Science Center, Jinan 250014 (China); Li, Lixiang [Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, P.O. Box 145, Beijing 100876 (China); National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Peng, Haipeng, E-mail: penghaipeng@bupt.edu.cn [Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, P.O. Box 145, Beijing 100876 (China); National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Luo, Qun; Yang, Yixian [Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, P.O. Box 145, Beijing 100876 (China); National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876 (China)
2014-02-01
This letter investigates the multiple routes transmitted epidemic process on multiplex networks. We propose detailed theoretical analysis that allows us to accurately calculate the epidemic threshold and outbreak size. It is found that the epidemic can spread across the multiplex network even if all the network layers are well below their respective epidemic thresholds. Strong positive degree–degree correlation of nodes in multiplex network could lead to a much lower epidemic threshold and a relatively smaller outbreak size. However, the average similarity of neighbors from different layers of nodes has no obvious effect on the epidemic threshold and outbreak size. -- Highlights: •We studies multiple routes transmitted epidemic process on multiplex networks. •SIR model and bond percolation theory are used to analyze the epidemic processes. •We derive equations to accurately calculate the epidemic threshold and outbreak size. •ASN has no effect on the epidemic threshold and outbreak size. •Strong positive DDC leads to a lower epidemic threshold and a smaller outbreak size.
Fractional virus epidemic model on financial networks
Directory of Open Access Journals (Sweden)
Balci Mehmet Ali
2016-01-01
Full Text Available In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.
Epidemic Spreading with Heterogeneous Awareness on Human Networks
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Yanling Lu
2017-01-01
Full Text Available The spontaneous awareness behavioral responses of individuals have a significant impact on epidemic spreading. In this paper, a modified Susceptible-Alert-Infected-Susceptible (SAIS epidemic model with heterogeneous awareness is presented to study epidemic spreading in human networks and the impact of heterogeneous awareness on epidemic dynamics. In this model, when susceptible individuals receive awareness information about the presence of epidemic from their infected neighbor nodes, they will become alert individuals with heterogeneous awareness rate. Theoretical analysis and numerical simulations show that heterogeneous awareness can enhance the epidemic threshold with certain conditions and reduce the scale of virus outbreaks compared with no awareness. What is more, for the same awareness parameter, it also shows that heterogeneous awareness can slow effectively the spreading size and does not delay the arrival time of epidemic spreading peak compared with homogeneous awareness.
Chu, A.
2016-12-01
Modern earthquake catalogs are often analyzed using spatial-temporal point process models such as the epidemic-type aftershock sequence (ETAS) models of Ogata (1998). My work implements three of the homogeneous ETAS models described in Ogata (1998). With a model's log-likelihood function, my software finds the Maximum-Likelihood Estimates (MLEs) of the model's parameters to estimate the homogeneous background rate and the temporal and spatial parameters that govern triggering effects. EM-algorithm is employed for its advantages of stability and robustness (Veen and Schoenberg, 2008). My work also presents comparisons among the three models in robustness, convergence speed, and implementations from theory to computing practice. Up-to-date regional seismic data of seismic active areas such as Southern California and Japan are used to demonstrate the comparisons. Data analysis has been done using computer languages Java and R. Java has the advantages of being strong-typed and easiness of controlling memory resources, while R has the advantages of having numerous available functions in statistical computing. Comparisons are also made between the two programming languages in convergence and stability, computational speed, and easiness of implementation. Issues that may affect convergence such as spatial shapes are discussed.
Global stability of an SEIR epidemic model with constant immigration
Energy Technology Data Exchange (ETDEWEB)
Li Guihua [Key Laboratory of Eco-environments in Three Gorges Reservoir Region (Ministry of Education), Faculty of Life Science, Southwest China Normal University, Chongqing 400715 (China) and Department of Mathematics, Southwest China Normal University, Chongqing 400715 (China) and Department of Mathematics, North University of China, Taiyuan Shanxi 030051 (China)]. E-mail: liguihua@nuc.edu.cn; Wang Wendi [Department of Mathematics, Southwest China Normal University, Chongqing 400715 (China); Jin Zhen [Department of Mathematics, North University of China, Taiyuan Shanxi 030051 (China)
2006-11-15
An SEIR epidemic model with the infectious force in the latent (exposed), infected and recovered period is studied. It is assumed that susceptible and exposed individuals have constant immigration rates. The model exhibits a unique endemic state if the fraction p of infectious immigrants is positive. If the basic reproduction number R is greater than 1, sufficient conditions for the global stability of the endemic equilibrium are obtained by the compound matrix theory.
Global stability of an SEIR epidemic model with constant immigration
International Nuclear Information System (INIS)
Li Guihua; Wang Wendi; Jin Zhen
2006-01-01
An SEIR epidemic model with the infectious force in the latent (exposed), infected and recovered period is studied. It is assumed that susceptible and exposed individuals have constant immigration rates. The model exhibits a unique endemic state if the fraction p of infectious immigrants is positive. If the basic reproduction number R is greater than 1, sufficient conditions for the global stability of the endemic equilibrium are obtained by the compound matrix theory
Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases
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Fazal Haq
2017-01-01
Full Text Available The fractional order Susceptible-Infected-Recovered (SIR epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.
Spreading speed and travelling waves for a spatially discrete SIS epidemic model
International Nuclear Information System (INIS)
Zhang, Kate Fang; Zhao Xiaoqiang
2008-01-01
This paper is devoted to the study of the asymptotic speed of spread and travelling waves for a spatially discrete SIS epidemic model. By appealing to the theory of spreading speeds and travelling waves for monotonic semiflows, we establish the existence of asymptotic speed of spread and show that it coincides with the minimal wave speed for monotonic travelling waves. This also gives an affirmative answer to an open problem presented by Rass and Radcliffe (2003 Spatial Deterministic Epidemics (Mathematical Surveys and Monographs vol 102) (Providence, RI: American Mathematical Society)) in the case of discrete spatial habitat
Disease spreading with epidemic alert on small-world networks
International Nuclear Information System (INIS)
Han, Xiao-Pu
2007-01-01
Base on two-dimension small-world networks, a susceptible-infected model with epidemic alert is proposed in this Letter. In this model, if some parts of the network are alarmed as dangerous, a fraction of edges between the alarmed parts and others will be removed, and two cases of alerting rules that the degree and frequency of contacts kept unchanged are considered respectively. The numerical simulations show that the spreading velocity is reduced by the accurate and timely epidemic alert, and the more accurate and timely, the stronger the deceleration effect. This model indicates that to broadcast epidemic alert timely is helpful and necessary in the control of epidemic spreading, and in agreement with the general view of epidemic alert. This work is helpful to understand the effects of epidemic alert on disease spreading
Critical behavior in a stochastic model of vector mediated epidemics
Alfinito, E.; Beccaria, M.; Macorini, G.
2016-06-01
The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.
Zhang, Juping; Yang, Chan; Jin, Zhen; Li, Jia
2018-07-14
In this paper, the correlation coefficients between nodes in states are used as dynamic variables, and we construct SIR epidemic dynamic models with correlation coefficients by using the pair approximation method in static networks and dynamic networks, respectively. Considering the clustering coefficient of the network, we analytically investigate the existence and the local asymptotic stability of each equilibrium of these models and derive threshold values for the prevalence of diseases. Additionally, we obtain two equivalent epidemic thresholds in dynamic networks, which are compared with the results of the mean field equations. Copyright © 2018 Elsevier Ltd. All rights reserved.
Epidemic cholera spreads like wildfire
Roy, Manojit; Zinck, Richard D.; Bouma, Menno J.; Pascual, Mercedes
2014-01-01
Cholera is on the rise globally, especially epidemic cholera which is characterized by intermittent and unpredictable outbreaks that punctuate periods of regional disease fade-out. These epidemic dynamics remain however poorly understood. Here we examine records for epidemic cholera over both contemporary and historical timelines, from Africa (1990-2006) and former British India (1882-1939). We find that the frequency distribution of outbreak size is fat-tailed, scaling approximately as a power-law. This pattern which shows strong parallels with wildfires is incompatible with existing cholera models developed for endemic regions, as it implies a fundamental role for stochastic transmission and local depletion of susceptible hosts. Application of a recently developed forest-fire model indicates that epidemic cholera dynamics are located above a critical phase transition and propagate in similar ways to aggressive wildfires. These findings have implications for the effectiveness of control measures and the mechanisms that ultimately limit the size of outbreaks.
Global dynamics of a dengue epidemic mathematical model
Energy Technology Data Exchange (ETDEWEB)
Cai Liming [Department of Mathematics, Xinyang Normal University, Xinyang 464000 (China); Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100080 (China)], E-mail: lmcai06@yahoo.com.cn; Guo Shumin [Beijing Institute of Information Control, Beijing 100037 (China); Li, XueZhi [Department of Mathematics, Xinyang Normal University, Xinyang 464000 (China); Ghosh, Mini [School of Mathematics and Computer Application, Thapar University, Patiala 147004 (India)
2009-11-30
The paper investigates the global stability of a dengue epidemic model with saturation and bilinear incidence. The constant human recruitment rate and exponential natural death, as well as vector population with asymptotically constant population, are incorporated into the model. The model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. The stability of these two equilibria is controlled by the threshold number R{sub 0}. It is shown that if R{sub 0} is less than one, the disease-free equilibrium is globally asymptotically stable and in such a case the endemic equilibrium does not exist; if R{sub 0} is greater than one, then the disease persists and the unique endemic equilibrium is globally asymptotically stable.
Can influenza epidemics be prevented by voluntary vaccination?
Directory of Open Access Journals (Sweden)
Raffaele Vardavas
2007-05-01
Full Text Available Previous modeling studies have identified the vaccination coverage level necessary for preventing influenza epidemics, but have not shown whether this critical coverage can be reached. Here we use computational modeling to determine, for the first time, whether the critical coverage for influenza can be achieved by voluntary vaccination. We construct a novel individual-level model of human cognition and behavior; individuals are characterized by two biological attributes (memory and adaptability that they use when making vaccination decisions. We couple this model with a population-level model of influenza that includes vaccination dynamics. The coupled models allow individual-level decisions to influence influenza epidemiology and, conversely, influenza epidemiology to influence individual-level decisions. By including the effects of adaptive decision-making within an epidemic model, we can reproduce two essential characteristics of influenza epidemiology: annual variation in epidemic severity and sporadic occurrence of severe epidemics. We suggest that individual-level adaptive decision-making may be an important (previously overlooked causal factor in driving influenza epidemiology. We find that severe epidemics cannot be prevented unless vaccination programs offer incentives. Frequency of severe epidemics could be reduced if programs provide, as an incentive to be vaccinated, several years of free vaccines to individuals who pay for one year of vaccination. Magnitude of epidemic amelioration will be determined by the number of years of free vaccination, an individuals' adaptability in decision-making, and their memory. This type of incentive program could control epidemics if individuals are very adaptable and have long-term memories. However, incentive-based programs that provide free vaccination for families could increase the frequency of severe epidemics. We conclude that incentive-based vaccination programs are necessary to control
Mean-field modeling approach for understanding epidemic dynamics in interconnected networks
International Nuclear Information System (INIS)
Zhu, Guanghu; Fu, Xinchu; Tang, Qinggan; Li, Kezan
2015-01-01
Modern systems (e.g., social, communicant, biological networks) are increasingly interconnected each other formed as ‘networks of networks’. Such complex systems usually possess inconsistent topologies and permit agents distributed in different subnetworks to interact directly/indirectly. Corresponding dynamics phenomena, such as the transmission of information, power, computer virus and disease, would exhibit complicated and heterogeneous tempo-spatial patterns. In this paper, we focus on the scenario of epidemic spreading in interconnected networks. We intend to provide a typical mean-field modeling framework to describe the time-evolution dynamics, and offer some mathematical skills to study the spreading threshold and the global stability of the model. Integrating the research with numerical analysis, we are able to quantify the effects of networks structure and epidemiology parameters on the transmission dynamics. Interestingly, we find that the diffusion transition in the whole network is governed by a unique threshold, which mainly depends on the most heterogenous connection patterns of network substructures. Further, the dynamics is highly sensitive to the critical values of cross infectivity with switchable phases.
Two approaches to forecast Ebola synthetic epidemics.
Champredon, David; Li, Michael; Bolker, Benjamin M; Dushoff, Jonathan
2018-03-01
We use two modelling approaches to forecast synthetic Ebola epidemics in the context of the RAPIDD Ebola Forecasting Challenge. The first approach is a standard stochastic compartmental model that aims to forecast incidence, hospitalization and deaths among both the general population and health care workers. The second is a model based on the renewal equation with latent variables that forecasts incidence in the whole population only. We describe fitting and forecasting procedures for each model and discuss their advantages and drawbacks. We did not find that one model was consistently better in forecasting than the other. Copyright © 2017 The Author(s). Published by Elsevier B.V. All rights reserved.
Epidemic Network Failures in Optical Transport Networks
DEFF Research Database (Denmark)
Ruepp, Sarah Renée; Katsikas, Dimitrios; Fagertun, Anna Manolova
2013-01-01
This paper presents a failure propagation model for transport networks which are affected by epidemic failures. The network is controlled using the GMPLS protocol suite. The Susceptible Infected Disabled (SID) epidemic model is investigated and new signaling functionality of GMPLS to support...
Understanding Ebola: the 2014 epidemic.
Kaner, Jolie; Schaack, Sarah
2016-09-13
Near the end of 2013, an outbreak of Zaire ebolavirus (EBOV) began in Guinea, subsequently spreading to neighboring Liberia and Sierra Leone. As this epidemic grew, important public health questions emerged about how and why this outbreak was so different from previous episodes. This review provides a synthetic synopsis of the 2014-15 outbreak, with the aim of understanding its unprecedented spread. We present a summary of the history of previous epidemics, describe the structure and genetics of the ebolavirus, and review our current understanding of viral vectors and the latest treatment practices. We conclude with an analysis of the public health challenges epidemic responders faced and some of the lessons that could be applied to future outbreaks of Ebola or other viruses.
Directory of Open Access Journals (Sweden)
Clement N Mweya
Full Text Available Rift Valley Fever (RVF is weather dependent arboviral infection of livestock and humans. Population dynamics of mosquito vectors is associated with disease epidemics. In our study, we use daily temperature and rainfall as model inputs to simulate dynamics of mosquito vectors population in relation to disease epidemics.Time-varying distributed delays (TVDD and multi-way functional response equations were implemented to simulate mosquito vectors and hosts developmental stages and to establish interactions between stages and phases of mosquito vectors in relation to vertebrate hosts for infection introduction in compartmental phases. An open-source modelling platforms, Universal Simulator and Qt integrated development environment were used to develop models in C++ programming language. Developed models include source codes for mosquito fecundity, host fecundity, water level, mosquito infection, host infection, interactions, and egg time. Extensible Markup Language (XML files were used as recipes to integrate source codes in Qt creator with Universal Simulator plug-in. We observed that Floodwater Aedines and Culicine population continued to fluctuate with temperature and water level over simulation period while controlled by availability of host for blood feeding. Infection in the system was introduced by floodwater Aedines. Culicines pick infection from infected host once to amplify disease epidemic. Simulated mosquito population show sudden unusual increase between December 1997 and January 1998 a similar period when RVF outbreak occurred in Ngorongoro district.Findings presented here provide new opportunities for weather-driven RVF epidemic simulation modelling. This is an ideal approach for understanding disease transmission dynamics towards epidemics prediction, prevention and control. This approach can be used as an alternative source for generation of calibrated RVF epidemics data in different settings.
Mweya, Clement N; Holst, Niels; Mboera, Leonard E G; Kimera, Sharadhuli I
2014-01-01
Rift Valley Fever (RVF) is weather dependent arboviral infection of livestock and humans. Population dynamics of mosquito vectors is associated with disease epidemics. In our study, we use daily temperature and rainfall as model inputs to simulate dynamics of mosquito vectors population in relation to disease epidemics. Time-varying distributed delays (TVDD) and multi-way functional response equations were implemented to simulate mosquito vectors and hosts developmental stages and to establish interactions between stages and phases of mosquito vectors in relation to vertebrate hosts for infection introduction in compartmental phases. An open-source modelling platforms, Universal Simulator and Qt integrated development environment were used to develop models in C++ programming language. Developed models include source codes for mosquito fecundity, host fecundity, water level, mosquito infection, host infection, interactions, and egg time. Extensible Markup Language (XML) files were used as recipes to integrate source codes in Qt creator with Universal Simulator plug-in. We observed that Floodwater Aedines and Culicine population continued to fluctuate with temperature and water level over simulation period while controlled by availability of host for blood feeding. Infection in the system was introduced by floodwater Aedines. Culicines pick infection from infected host once to amplify disease epidemic. Simulated mosquito population show sudden unusual increase between December 1997 and January 1998 a similar period when RVF outbreak occurred in Ngorongoro district. Findings presented here provide new opportunities for weather-driven RVF epidemic simulation modelling. This is an ideal approach for understanding disease transmission dynamics towards epidemics prediction, prevention and control. This approach can be used as an alternative source for generation of calibrated RVF epidemics data in different settings.
Modelling dengue epidemic spreading with human mobility
Barmak, D. H.; Dorso, C. O.; Otero, M.
2016-04-01
We explored the effect of human mobility on the spatio-temporal dynamics of Dengue with a stochastic model that takes into account the epidemiological dynamics of the infected mosquitoes and humans, with different mobility patterns of the human population. We observed that human mobility strongly affects the spread of infection by increasing the final size and by changing the morphology of the epidemic outbreaks. When the spreading of the disease is driven only by mosquito dispersal (flight), a main central focus expands diffusively. On the contrary, when human mobility is taken into account, multiple foci appear throughout the evolution of the outbreaks. These secondary foci generated throughout the outbreaks could be of little importance according to their mass or size compared with the largest main focus. However, the coalescence of these foci with the main one generates an effect, through which the latter develops a size greater than the one obtained in the case driven only by mosquito dispersal. This increase in growth rate due to human mobility and the coalescence of the foci are particularly relevant in temperate cities such as the city of Buenos Aires, since they give more possibilities to the outbreak to grow before the arrival of the low-temperature season. The findings of this work indicate that human mobility could be the main driving force in the dynamics of vector epidemics.
Configuring the autism epidemic
DEFF Research Database (Denmark)
Seeberg, Jens; Christensen, Fie Lund Lindegaard
2017-01-01
Autism has been described as an epidemic, but this claim is contested and may point to an awareness epidemic, i.e. changes in the definition of what autism is and more attention being invested in diagnosis leading to a rise in registered cases. The sex ratio of children diagnosed with autism...... is skewed in favour of boys, and girls with autism tend to be diagnosed much later than boys. Building and further developing the notion of ‘configuration’ of epidemics, this article explores the configuration of autism in Denmark, with a particular focus on the health system and social support to families...... with children diagnosed with autism, seen from a parental perspective. The article points to diagnostic dynamics that contribute to explaining why girls with autism are not diagnosed as easily as boys. We unfold these dynamics through the analysis of a case of a Danish family with autism....
Emergence of epidemics in rapidly varying networks
International Nuclear Information System (INIS)
Kohar, Vivek; Sinha, Sudeshna
2013-01-01
We describe a simple model mimicking disease spreading on a network with dynamically varying connections, and investigate the dynamical consequences of switching links in the network. Our central observation is that the disease cycles get more synchronized, indicating the onset of epidemics, as the underlying network changes more rapidly. This behavior is found for periodically switched links, as well as links that switch randomly in time. We find that the influence of changing links is more pronounced in networks where the nodes have lower degree, and the disease cycle has a longer infective stage. Further, when the switching of links is periodic we observe finer dynamical features, such as beating patterns in the emergent oscillations and resonant enhancement of synchronization, arising from the interplay between the time-scales of the connectivity changes and that of the epidemic outbreaks
Trajanovski, S.; Guo, D.; Van Mieghem, P.F.A.
2015-01-01
The continuous-time adaptive susceptible-infected-susceptible (ASIS) epidemic model and the adaptive information diffusion (AID) model are two adaptive spreading processes on networks, in which a link in the network changes depending on the infectious state of its end nodes, but in opposite ways:
Hopf Bifurcation of a Delayed Epidemic Model with Information Variable and Limited Medical Resources
Directory of Open Access Journals (Sweden)
Caijuan Yan
2014-01-01
Full Text Available We consider SIR epidemic model in which population growth is subject to logistic growth in absence of disease. We get the condition for Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. If the basic reproduction ratio ℛ01, we obtain sufficient conditions under which the endemic equilibrium E* of system is locally asymptotically stable. And we also have discussed the stability and direction of Hopf bifurcations. Numerical simulations are carried out to explain the mathematical conclusions.
Blower, Sally; Go, Myong-Hyun
2011-01-01
Abstract Mathematical models are useful tools for understanding and predicting epidemics. A recent innovative modeling study by Stehle and colleagues addressed the issue of how complex models need to be to ensure accuracy. The authors collected data on face-to-face contacts during a two-day conference. They then constructed a series of dynamic social contact networks, each of which was used to model an epidemic generated by a fast-spreading airborne pathogen. Intriguingly, Stehle and colleagu...
Permanence for a Delayed Nonautonomous SIR Epidemic Model with Density-Dependent Birth Rate
Directory of Open Access Journals (Sweden)
Li Yingke
2011-01-01
Full Text Available Based on some well-known SIR models, a revised nonautonomous SIR epidemic model with distributed delay and density-dependent birth rate was considered. Applying some classical analysis techniques for ordinary differential equations and the method proposed by Wang (2002, the threshold value for the permanence and extinction of the model was obtained.
Dynamics of tax evasion through an epidemic-like model
Brum, Rafael M.; Crokidakis, Nuno
In this work, we study a model of tax evasion. We considered a fixed population divided in three compartments, namely honest tax payers, tax evaders and a third class between the mentioned two, which we call susceptibles to become evaders. The transitions among those compartments are ruled by probabilities, similarly to a model of epidemic spreading. These probabilities model social interactions among the individuals, as well as the government’s fiscalization. We simulate the model on fully-connected graphs, as well as on scale-free and random complex networks. For the fully-connected and random graph cases, we observe that the emergence of tax evaders in the population is associated with an active-absorbing nonequilibrium phase transition, that is absent in scale-free networks.
Inferring epidemic contact structure from phylogenetic trees.
Directory of Open Access Journals (Sweden)
Gabriel E Leventhal
Full Text Available Contact structure is believed to have a large impact on epidemic spreading and consequently using networks to model such contact structure continues to gain interest in epidemiology. However, detailed knowledge of the exact contact structure underlying real epidemics is limited. Here we address the question whether the structure of the contact network leaves a detectable genetic fingerprint in the pathogen population. To this end we compare phylogenies generated by disease outbreaks in simulated populations with different types of contact networks. We find that the shape of these phylogenies strongly depends on contact structure. In particular, measures of tree imbalance allow us to quantify to what extent the contact structure underlying an epidemic deviates from a null model contact network and illustrate this in the case of random mixing. Using a phylogeny from the Swiss HIV epidemic, we show that this epidemic has a significantly more unbalanced tree than would be expected from random mixing.
International Nuclear Information System (INIS)
Li, Jinhui; Teng, Zhidong; Wang, Guangqing; Zhang, Long; Hu, Cheng
2017-01-01
In this paper, we introduce the saturated treatment and logistic growth rate into an SIR epidemic model with bilinear incidence. The treatment function is assumed to be a continuously differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large enough. Sufficient conditions for the existence and local stability of the disease-free and positive equilibria are established. And the existence of the stable limit cycles also is obtained. Moreover, by using the theory of bifurcations, it is shown that the model exhibits backward bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcations. Finally, the numerical examples are given to illustrate the theoretical results and obtain some additional interesting phenomena, involving double stable periodic solutions and stable limit cycles.
Heterogeneous Epidemic Model for Assessing Data Dissemination in Opportunistic Networks
DEFF Research Database (Denmark)
Rozanova, Liudmila; Alekseev, Vadim; Temerev, Alexander
2014-01-01
that amount of data transferred between network nodes possesses a Pareto distribution, implying scale-free properties. In this context, more heterogeneity in susceptibility means the less severe epidemic progression, and, on the contrary, more heterogeneity in infectivity leads to more severe epidemics...... — assuming that the other parameter (either heterogeneity or susceptibility) stays fixed. The results are general enough to be useful for estimating the epidemic progression with no significant acquired immunity — in the cases where Pareto distribution holds....
Mathematical modeling of Avian Influenza epidemic with bird vaccination in constant population
Kharis, M.; Amidi
2018-03-01
The development of the industrial world and human life is increasingly modern and less attention to environmental sustainability causes the virus causes the epidemic has a high tendency to mutate so that the virus that initially only attack animals, is also found to have the ability to attack humans. The epidemics that lasted some time were bird flu epidemics and swine flu epidemics. The flu epidemic led to several deaths and many people admitted to the hospital. Strain (derivatives) of H5N1 virus was identified as the cause of the bird flu epidemic while the H1N1 strain of the virus was identified as the cause of the swine flu epidemic. The symptoms are similar to seasonal flu caused by H3N2 strain of the virus. Outbreaks of bird flu and swine flu initially only attacked animals, but over time some people were found to be infected with the virus.
Existence, uniqueness, monotonicity and asymptotic behaviour of travelling waves for epidemic models
International Nuclear Information System (INIS)
Hsu, Cheng-Hsiung; Yang, Tzi-Sheng
2013-01-01
The purpose of this work is to investigate the existence, uniqueness, monotonicity and asymptotic behaviour of travelling wave solutions for a general epidemic model arising from the spread of an epidemic by oral–faecal transmission. First, we apply Schauder's fixed point theorem combining with a supersolution and subsolution pair to derive the existence of positive monotone monostable travelling wave solutions. Then, applying the Ikehara's theorem, we determine the exponential rates of travelling wave solutions which converge to two different equilibria as the moving coordinate tends to positive infinity and negative infinity, respectively. Finally, using the sliding method, we prove the uniqueness result provided the travelling wave solutions satisfy some boundedness conditions. (paper)
Modelling cholera epidemics: the role of waterways, human mobility and sanitation
Mari, L.; Bertuzzo, E.; Righetto, L.; Casagrandi, R.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.
2011-01-01
We investigate the role of human mobility as a driver for long-range spreading of cholera infections, which primarily propagate through hydrologically controlled ecological corridors. Our aim is to build a spatially explicit model of a disease epidemic, which is relevant to both social and scientific issues. We present a two-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of the pathogen Vibrio choler...
Dynamics of epidemic spreading model with drug-resistant variation on scale-free networks
Wan, Chen; Li, Tao; Zhang, Wu; Dong, Jing
2018-03-01
Considering the influence of the virus' drug-resistant variation, a novel SIVRS (susceptible-infected-variant-recovered-susceptible) epidemic spreading model with variation characteristic on scale-free networks is proposed in this paper. By using the mean-field theory, the spreading dynamics of the model is analyzed in detail. Then, the basic reproductive number R0 and equilibriums are derived. Studies show that the existence of disease-free equilibrium is determined by the basic reproductive number R0. The relationships between the basic reproductive number R0, the variation characteristic and the topology of the underlying networks are studied in detail. Furthermore, our studies prove the global stability of the disease-free equilibrium, the permanence of epidemic and the global attractivity of endemic equilibrium. Numerical simulations are performed to confirm the analytical results.
Oscillations in epidemic models with spread of awareness.
Just, Winfried; Saldaña, Joan; Xin, Ying
2018-03-01
We study ODE models of epidemic spreading with a preventive behavioral response that is triggered by awareness of the infection. Previous studies of such models have mostly focused on the impact of the response on the initial growth of an outbreak and the existence and location of endemic equilibria. Here we study the question whether this type of response is sufficient to prevent future flare-ups from low endemic levels if awareness is assumed to decay over time. In the ODE context, such flare-ups would translate into sustained oscillations with significant amplitudes. Our results show that such oscillations are ruled out in Susceptible-Aware-Infectious-Susceptible models with a single compartment of aware hosts, but can occur if we consider two distinct compartments of aware hosts who differ in their willingness to alert other susceptible hosts.
Non-homogeneous stochastic birth and death processes with applications to epidemic outbreak data
van den Broek, J.
2012-01-01
The subject of this thesis is the non-homogeneous birth-death process with some of its special cases and its use in modeling epidemic data. This model describes changes in the size of a population. New population members can appear with a rate, called the birth rate or the reproductive power, and
Can rewiring strategy control the epidemic spreading?
Dong, Chao; Yin, Qiuju; Liu, Wenyang; Yan, Zhijun; Shi, Tianyu
2015-11-01
Relation existed in the social contact network can affect individuals' behaviors greatly. Considering the diversity of relation intimacy among network nodes, an epidemic propagation model is proposed by incorporating the link-breaking threshold, which is normally neglected in the rewiring strategy. The impact of rewiring strategy on the epidemic spreading in the weighted adaptive network is explored. The results show that the rewiring strategy cannot always control the epidemic prevalence, especially when the link-breaking threshold is low. Meanwhile, as well as strong links, weak links also play a significant role on epidemic spreading.
MOSES: A Matlab-based open-source stochastic epidemic simulator.
Varol, Huseyin Atakan
2016-08-01
This paper presents an open-source stochastic epidemic simulator. Discrete Time Markov Chain based simulator is implemented in Matlab. The simulator capable of simulating SEQIJR (susceptible, exposed, quarantined, infected, isolated and recovered) model can be reduced to simpler models by setting some of the parameters (transition probabilities) to zero. Similarly, it can be extended to more complicated models by editing the source code. It is designed to be used for testing different control algorithms to contain epidemics. The simulator is also designed to be compatible with a network based epidemic simulator and can be used in the network based scheme for the simulation of a node. Simulations show the capability of reproducing different epidemic model behaviors successfully in a computationally efficient manner.
Time Prediction Models for Echinococcosis Based on Gray System Theory and Epidemic Dynamics.
Zhang, Liping; Wang, Li; Zheng, Yanling; Wang, Kai; Zhang, Xueliang; Zheng, Yujian
2017-03-04
Echinococcosis, which can seriously harm human health and animal husbandry production, has become an endemic in the Xinjiang Uygur Autonomous Region of China. In order to explore an effective human Echinococcosis forecasting model in Xinjiang, three grey models, namely, the traditional grey GM(1,1) model, the Grey-Periodic Extensional Combinatorial Model (PECGM(1,1)), and the Modified Grey Model using Fourier Series (FGM(1,1)), in addition to a multiplicative seasonal ARIMA(1,0,1)(1,1,0)₄ model, are applied in this study for short-term predictions. The accuracy of the different grey models is also investigated. The simulation results show that the FGM(1,1) model has a higher performance ability, not only for model fitting, but also for forecasting. Furthermore, considering the stability and the modeling precision in the long run, a dynamic epidemic prediction model based on the transmission mechanism of Echinococcosis is also established for long-term predictions. Results demonstrate that the dynamic epidemic prediction model is capable of identifying the future tendency. The number of human Echinococcosis cases will increase steadily over the next 25 years, reaching a peak of about 1250 cases, before eventually witnessing a slow decline, until it finally ends.
Time Prediction Models for Echinococcosis Based on Gray System Theory and Epidemic Dynamics
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Liping Zhang
2017-03-01
Full Text Available Echinococcosis, which can seriously harm human health and animal husbandry production, has become an endemic in the Xinjiang Uygur Autonomous Region of China. In order to explore an effective human Echinococcosis forecasting model in Xinjiang, three grey models, namely, the traditional grey GM(1,1 model, the Grey-Periodic Extensional Combinatorial Model (PECGM(1,1, and the Modified Grey Model using Fourier Series (FGM(1,1, in addition to a multiplicative seasonal ARIMA(1,0,1(1,1,04 model, are applied in this study for short-term predictions. The accuracy of the different grey models is also investigated. The simulation results show that the FGM(1,1 model has a higher performance ability, not only for model fitting, but also for forecasting. Furthermore, considering the stability and the modeling precision in the long run, a dynamic epidemic prediction model based on the transmission mechanism of Echinococcosis is also established for long-term predictions. Results demonstrate that the dynamic epidemic prediction model is capable of identifying the future tendency. The number of human Echinococcosis cases will increase steadily over the next 25 years, reaching a peak of about 1250 cases, before eventually witnessing a slow decline, until it finally ends.
The Role of Node Heterogeneity in the Coupled Spreading of Epidemics and Awareness.
Guo, Quantong; Lei, Yanjun; Xia, Chengyi; Guo, Lu; Jiang, Xin; Zheng, Zhiming
2016-01-01
Exploring the interplay between information spreading and epidemic spreading is a topic that has been receiving increasing attention. As an efficient means of depicting the spreading of information, which manifests as a cascade phenomenon, awareness cascading is utilized to investigate this coupled transmission. Because in reality, different individuals facing the same epidemic will exhibit distinct behaviors according to their own experiences and attributes, it is important for us to consider the heterogeneity of individuals. Consequently, we propose a heterogeneous spreading model. To describe the heterogeneity, two of the most important but radically different methods for this purpose, the degree and k-core measures, are studied in this paper through three models based on different assumptions. Adopting a Markov chain approach, we succeed in predicting the epidemic threshold trend. Furthermore, we find that when the k-core measure is used to classify individuals, the spreading process is robust to these models, meaning that regardless of the model used, the spreading process is nearly identical at the macroscopic level. In addition, the k-core measure leads to a much larger final epidemic size than the degree measure. These results are cross-checked through numerous simulations, not only of a synthetic network but also of a real multiplex network. The presented findings provide a better understanding of k-core individuals and reveal the importance of considering network structure when investigating various dynamic processes.
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El Doma, M.
1995-05-01
An age-structured epidemic model of an SI type that incorporate vertical transmission is investigated when the fertility and mortality rates depend on age. We determine the steady states and examine their stabilities. (author). 13 refs
Optimal control and stability analysis of an epidemic model with population dispersal
International Nuclear Information System (INIS)
Jana, Soovoojeet; Haldar, Palash; Kar, T.K.
2016-01-01
Highlights: • SEIR type epidemic model with population dispersal is considered here. • Vaccination is taken as a control parameter. • Optimal control problem is formulated and then solved. • Simulation shows that different diseases can be analyzed through this model. - Abstract: In the present paper we consider an SEIR type epidemic model with transport related infection between two cities. It is observed that transportation among regions has a strong impact on the dynamic evolution of a disease which can be eradicated in the absence of transportation. Transportation can lead to the incorporation of a positive risk probability. The epidemiological threshold, commonly known as the basic reproduction number, is derived and it is observed that when the basic reproduction number is less than unity the disease dies out, where as if it exceeds unity the disease may persist in the system. A thorough dynamical behavior of the constructed model is studied. We formulate and solve an optimal control problem using vaccination as a control tool. Extensive numerical simulations are carried out based on our analytical results. Finally we try to relate our work with a real world problem.
Improved bounds on the epidemic threshold of exact SIS models on complex networks
Ruhi, Navid Azizan; Thrampoulidis, Christos; Hassibi, Babak
2017-01-01
The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λmax(A) is the largest eigenvalue of the network's adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.
Improved bounds on the epidemic threshold of exact SIS models on complex networks
Ruhi, Navid Azizan
2017-01-05
The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λmax(A) is the largest eigenvalue of the network\\'s adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.
Disease Extinction Versus Persistence in Discrete-Time Epidemic Models.
van den Driessche, P; Yakubu, Abdul-Aziz
2018-04-12
We focus on discrete-time infectious disease models in populations that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations, and give a method for computing the basic reproduction number, [Formula: see text]. When [Formula: see text] and the demographic population dynamics are asymptotically constant or under geometric growth (non-oscillatory), we prove global asymptotic stability of the disease-free equilibrium of the disease models. Under the same demographic assumption, when [Formula: see text], we prove uniform persistence of the disease. We apply our theoretical results to specific discrete-time epidemic models that are formulated for SEIR infections, cholera in humans and anthrax in animals. Our simulations show that a unique endemic equilibrium of each of the three specific disease models is asymptotically stable whenever [Formula: see text].
An, Qingyu; Wu, Jun; Fan, Xuesong; Pan, Liyang; Sun, Wei
2016-01-01
The hand foot and mouth disease (HFMD) is a human syndrome caused by intestinal viruses like that coxsackie A virus 16, enterovirus 71 and easily developed into outbreak in kindergarten and school. Scientifically and accurately early detection of the start time of HFMD epidemic is a key principle in planning of control measures and minimizing the impact of HFMD. The objective of this study was to establish a reliable early detection model for start timing of hand foot mouth disease epidemic in Dalian and to evaluate the performance of model by analyzing the sensitivity in detectability. The negative binomial regression model was used to estimate the weekly baseline case number of HFMD and identified the optimal alerting threshold between tested difference threshold values during the epidemic and non-epidemic year. Circular distribution method was used to calculate the gold standard of start timing of HFMD epidemic. From 2009 to 2014, a total of 62022 HFMD cases were reported (36879 males and 25143 females) in Dalian, Liaoning Province, China, including 15 fatal cases. The median age of the patients was 3 years. The incidence rate of epidemic year ranged from 137.54 per 100,000 population to 231.44 per 100,000population, the incidence rate of non-epidemic year was lower than 112 per 100,000 population. The negative binomial regression model with AIC value 147.28 was finally selected to construct the baseline level. The threshold value was 100 for the epidemic year and 50 for the non- epidemic year had the highest sensitivity(100%) both in retrospective and prospective early warning and the detection time-consuming was 2 weeks before the actual starting of HFMD epidemic. The negative binomial regression model could early warning the start of a HFMD epidemic with good sensitivity and appropriate detection time in Dalian.
Epidemic spreading on weighted complex networks
International Nuclear Information System (INIS)
Sun, Ye; Liu, Chuang; Zhang, Chu-Xu; Zhang, Zi-Ke
2014-01-01
Nowadays, the emergence of online services provides various multi-relation information to support the comprehensive understanding of the epidemic spreading process. In this Letter, we consider the edge weights to represent such multi-role relations. In addition, we perform detailed analysis of two representative metrics, outbreak threshold and epidemic prevalence, on SIS and SIR models. Both theoretical and simulation results find good agreements with each other. Furthermore, experiments show that, on fully mixed networks, the weight distribution on edges would not affect the epidemic results once the average weight of whole network is fixed. This work may shed some light on the in-depth understanding of epidemic spreading on multi-relation and weighted networks.
Epidemic spreading on weighted complex networks
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Sun, Ye [Institute of Information Economy, Hangzhou Normal University, Hangzhou 311121 (China); Alibaba Research Center of Complexity Science, Hangzhou Normal University, Hangzhou 311121 (China); Liu, Chuang, E-mail: liuchuang@hznu.edu.cn [Institute of Information Economy, Hangzhou Normal University, Hangzhou 311121 (China); Alibaba Research Center of Complexity Science, Hangzhou Normal University, Hangzhou 311121 (China); Zhang, Chu-Xu [Institute of Information Economy, Hangzhou Normal University, Hangzhou 311121 (China); Alibaba Research Center of Complexity Science, Hangzhou Normal University, Hangzhou 311121 (China); Zhang, Zi-Ke, E-mail: zhangzike@gmail.com [Institute of Information Economy, Hangzhou Normal University, Hangzhou 311121 (China); Alibaba Research Center of Complexity Science, Hangzhou Normal University, Hangzhou 311121 (China)
2014-01-31
Nowadays, the emergence of online services provides various multi-relation information to support the comprehensive understanding of the epidemic spreading process. In this Letter, we consider the edge weights to represent such multi-role relations. In addition, we perform detailed analysis of two representative metrics, outbreak threshold and epidemic prevalence, on SIS and SIR models. Both theoretical and simulation results find good agreements with each other. Furthermore, experiments show that, on fully mixed networks, the weight distribution on edges would not affect the epidemic results once the average weight of whole network is fixed. This work may shed some light on the in-depth understanding of epidemic spreading on multi-relation and weighted networks.
Dynamical Analysis of SIR Epidemic Models with Distributed Delay
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Wencai Zhao
2013-01-01
Full Text Available SIR epidemic models with distributed delay are proposed. Firstly, the dynamical behaviors of the model without vaccination are studied. Using the Jacobian matrix, the stability of the equilibrium points of the system without vaccination is analyzed. The basic reproduction number R is got. In order to study the important role of vaccination to prevent diseases, the model with distributed delay under impulsive vaccination is formulated. And the sufficient conditions of globally asymptotic stability of “infection-free” periodic solution and the permanence of the model are obtained by using Floquet’s theorem, small-amplitude perturbation skills, and comparison theorem. Lastly, numerical simulation is presented to illustrate our main conclusions that vaccination has significant effects on the dynamical behaviors of the model. The results can provide effective tactic basis for the practical infectious disease prevention.
Holb, I.J.; Heijne, B.; Jeger, M.J.
2003-01-01
A 2-year study on epidemic progress of apple scab was conducted at Randwijk, the Netherlands, in 1998 and 1999. The summer epidemic caused by conidia was studied instead of the well-described spring season epidemic originating from ascospores. The aim was to investigate relationships between disease
Household demographic determinants of Ebola epidemic risk.
Adams, Ben
2016-03-07
A salient characteristic of Ebola, and some other infectious diseases such as Tuberculosis, is intense transmission among small groups of cohabitants and relatively limited indiscriminate transmission in the wider population. Here we consider a mathematical model for an Ebola epidemic in a population structured into households of equal size. We show that household size, a fundamental demographic unit, is a critical factor that determines the vulnerability of a community to epidemics, and the effort required to control them. Our analysis is based on the household reproduction number, but we also consider the basic reproduction number, intrinsic growth rate and final epidemic size. We show that, when other epidemiological parameters are kept the same, all of these quantifications of epidemic growth and size are increased by larger households and more intense within-household transmission. We go on to model epidemic control by case detection and isolation followed by household quarantine. We show that, if household quarantine is ineffective, the critical probability with which cases must be detected to halt an epidemic increases significantly with each increment in household size and may be a very challenging target for communities composed of large households. Effective quarantine may, however, mitigate the detrimental impact of large household sizes. We conclude that communities composed of large households are fundamentally more vulnerable to epidemics of infectious diseases primarily transmitted by close contact, and any assessment of control strategies for these epidemics should take into account the demographic structure of the population. Copyright © 2015 Elsevier Ltd. All rights reserved.
Modeling the effects of social impact on epidemic spreading in complex networks
Ni, Shunjiang; Weng, Wenguo; Zhang, Hui
2011-11-01
We investigate by mean-field analysis and extensive simulations the effects of social impact on epidemic spreading in various typical networks with two types of nodes: active nodes and passive nodes, of which the behavior patterns are modeled according to the social impact theory. In this study, nodes are not only the media to spread the virus, but also disseminate their opinions on the virus-whether there is a need for certain self-protection measures to be taken to reduce the risk of being infected. Our results indicate that the interaction between epidemic spreading and opinion dynamics can have significant influences on the spreading of infectious diseases and related applications, such as the implementation of prevention and control measures against the infectious diseases.
Epidemic spreading in localized environments with recurrent mobility patterns
Granell, Clara; Mucha, Peter J.
2018-05-01
The spreading of epidemics is very much determined by the structure of the contact network, which may be impacted by the mobility dynamics of the individuals themselves. In confined scenarios where a small, closed population spends most of its time in localized environments and has easily identifiable mobility patterns—such as workplaces, university campuses, or schools—it is of critical importance to identify the factors controlling the rate of disease spread. Here, we present a discrete-time, metapopulation-based model to describe the transmission of susceptible-infected-susceptible-like diseases that take place in confined scenarios where the mobilities of the individuals are not random but, rather, follow clear recurrent travel patterns. This model allows analytical determination of the onset of epidemics, as well as the ability to discern which contact structures are most suited to prevent the infection to spread. It thereby determines whether common prevention mechanisms, as isolation, are worth implementing in such a scenario and their expected impact.
Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar
2018-02-01
In this paper, we study the dynamics of a stochastic delayed SIR epidemic model with vaccination and double diseases which make the research more complex. The environment variability in this paper is characterized by white noise and Lévy noise. We establish sufficient conditions for extinction and persistence in the mean of the two epidemic diseases. It is shown that: (i) time delay and Lévy noise have important effects on the persistence and extinction of epidemic diseases; (ii) two diseases can coexist under certain conditions.
Stability and bifurcation of an SIS epidemic model with treatment
International Nuclear Information System (INIS)
Li Xuezhi; Li Wensheng; Ghosh, Mini
2009-01-01
An SIS epidemic model with a limited resource for treatment is introduced and analyzed. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.
Epidemic Spread in Networks Induced by Deactivation Mechanism
International Nuclear Information System (INIS)
Yu Xiaoling; Wu Xiao; Zhang Duanming; Li Zhihao; Liang Fang; Wang Xiaoyu
2008-01-01
We have studied the topology and epidemic spreading behaviors on the networks in which deactivation mechanism and long-rang connection are coexisted. By means of numerical simulation, we find that the clustering coefficient C and the Pearson correlation coefficient r decrease with increasing long-range connection μ and the topological state of the network changes into that of BA model at the end (when μ = 1). For the Susceptible-Infect-Susceptible model of epidemics, the epidemic threshold can reach maximum value at μ = 0.4 and presents two different variable states around μ = 0.4
Epidemic dynamics and endemic states in complex networks
Pastor-Satorras, Romualdo; Vespignani, Alessandro
2001-06-01
We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. In networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null. On the contrary, on a wide range of scale-free networks we observe the absence of an epidemic threshold and its associated critical behavior. This implies that scale-free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess. These results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks.
Epidemic dynamics and endemic states in complex networks
International Nuclear Information System (INIS)
Pastor-Satorras, Romualdo; Vespignani, Alessandro
2001-01-01
We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. In networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null. On the contrary, on a wide range of scale-free networks we observe the absence of an epidemic threshold and its associated critical behavior. This implies that scale-free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess. These results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks
An epidemic model of rumor diffusion in online social networks
Cheng, Jun-Jun; Liu, Yun; Shen, Bo; Yuan, Wei-Guo
2013-01-01
So far, in some standard rumor spreading models, the transition probability from ignorants to spreaders is always treated as a constant. However, from a practical perspective, the case that individual whether or not be infected by the neighbor spreader greatly depends on the trustiness of ties between them. In order to solve this problem, we introduce a stochastic epidemic model of the rumor diffusion, in which the infectious probability is defined as a function of the strength of ties. Moreover, we investigate numerically the behavior of the model on a real scale-free social site with the exponent γ = 2.2. We verify that the strength of ties plays a critical role in the rumor diffusion process. Specially, selecting weak ties preferentially cannot make rumor spread faster and wider, but the efficiency of diffusion will be greatly affected after removing them. Another significant finding is that the maximum number of spreaders max( S) is very sensitive to the immune probability μ and the decay probability v. We show that a smaller μ or v leads to a larger spreading of the rumor, and their relationships can be described as the function ln(max( S)) = Av + B, in which the intercept B and the slope A can be fitted perfectly as power-law functions of μ. Our findings may offer some useful insights, helping guide the application in practice and reduce the damage brought by the rumor.
Predicting Subnational Ebola Virus Disease Epidemic Dynamics from Sociodemographic Indicators.
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Linda Valeri
Full Text Available The recent Ebola virus disease (EVD outbreak in West Africa has spread wider than any previous human EVD epidemic. While individual-level risk factors that contribute to the spread of EVD have been studied, the population-level attributes of subnational regions associated with outbreak severity have not yet been considered.To investigate the area-level predictors of EVD dynamics, we integrated time series data on cumulative reported cases of EVD from the World Health Organization and covariate data from the Demographic and Health Surveys. We first estimated the early growth rates of epidemics in each second-level administrative district (ADM2 in Guinea, Sierra Leone and Liberia using exponential, logistic and polynomial growth models. We then evaluated how these growth rates, as well as epidemic size within ADM2s, were ecologically associated with several demographic and socio-economic characteristics of the ADM2, using bivariate correlations and multivariable regression models.The polynomial growth model appeared to best fit the ADM2 epidemic curves, displaying the lowest residual standard error. Each outcome was associated with various regional characteristics in bivariate models, however in stepwise multivariable models only mean education levels were consistently associated with a worse local epidemic.By combining two common methods-estimation of epidemic parameters using mathematical models, and estimation of associations using ecological regression models-we identified some factors predicting rapid and severe EVD epidemics in West African subnational regions. While care should be taken interpreting such results as anything more than correlational, we suggest that our approach of using data sources that were publicly available in advance of the epidemic or in real-time provides an analytic framework that may assist countries in understanding the dynamics of future outbreaks as they occur.
Spatiotemporal modelling and mapping of the bubonic plague epidemic in India
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Christakos George
2006-03-01
Full Text Available Abstract Background This work studies the spatiotemporal evolution of bubonic plague in India during 1896–1906 using stochastic concepts and geographical information science techniques. In the past, most investigations focused on selected cities to conduct different kinds of studies, such as the ecology of rats. No detailed maps existed incorporating the space-time dependence structure and uncertainty sources of the epidemic system and providing a composite space-time picture of the disease propagation characteristics. Results Informative spatiotemporal maps were generated that represented mortality rates and geographical spread of the disease, and epidemic indicator plots were derived that offered meaningful characterizations of the spatiotemporal disease distribution. The bubonic plague in India exhibited strong seasonal and geographical features. During its entire duration, the plague continued to invade new geographical areas, while it followed a re-emergence pattern at many localities; its rate changed significantly during each year and the mortality distribution exhibited space-time heterogeneous patterns; prevalence usually occurred in the autumn and spring, whereas the plague stopped moving towards new locations during the summers. Conclusion Modern stochastic modelling and geographical information science provide powerful means to study the spatiotemporal distribution of the bubonic plague epidemic under conditions of uncertainty and multi-sourced databases; to account for various forms of interdisciplinary knowledge; and to generate informative space-time maps of mortality rates and propagation patterns. To the best of our knowledge, this kind of plague maps and plots become available for the first time, thus providing novel perspectives concerning the distribution and space-time propagation of the deadly epidemic. Furthermore, systematic maps and indicator plots make possible the comparison of the spatial-temporal propagation
Resource allocation for epidemic control in metapopulations.
Ndeffo Mbah, Martial L; Gilligan, Christopher A
2011-01-01
Deployment of limited resources is an issue of major importance for decision-making in crisis events. This is especially true for large-scale outbreaks of infectious diseases. Little is known when it comes to identifying the most efficient way of deploying scarce resources for control when disease outbreaks occur in different but interconnected regions. The policy maker is frequently faced with the challenge of optimizing efficiency (e.g. minimizing the burden of infection) while accounting for social equity (e.g. equal opportunity for infected individuals to access treatment). For a large range of diseases described by a simple SIRS model, we consider strategies that should be used to minimize the discounted number of infected individuals during the course of an epidemic. We show that when faced with the dilemma of choosing between socially equitable and purely efficient strategies, the choice of the control strategy should be informed by key measurable epidemiological factors such as the basic reproductive number and the efficiency of the treatment measure. Our model provides new insights for policy makers in the optimal deployment of limited resources for control in the event of epidemic outbreaks at the landscape scale.
Resource allocation for epidemic control in metapopulations.
Directory of Open Access Journals (Sweden)
Martial L Ndeffo Mbah
Full Text Available Deployment of limited resources is an issue of major importance for decision-making in crisis events. This is especially true for large-scale outbreaks of infectious diseases. Little is known when it comes to identifying the most efficient way of deploying scarce resources for control when disease outbreaks occur in different but interconnected regions. The policy maker is frequently faced with the challenge of optimizing efficiency (e.g. minimizing the burden of infection while accounting for social equity (e.g. equal opportunity for infected individuals to access treatment. For a large range of diseases described by a simple SIRS model, we consider strategies that should be used to minimize the discounted number of infected individuals during the course of an epidemic. We show that when faced with the dilemma of choosing between socially equitable and purely efficient strategies, the choice of the control strategy should be informed by key measurable epidemiological factors such as the basic reproductive number and the efficiency of the treatment measure. Our model provides new insights for policy makers in the optimal deployment of limited resources for control in the event of epidemic outbreaks at the landscape scale.
Dynamics of an epidemic model with quarantine on scale-free networks
Kang, Huiyan; Liu, Kaihui; Fu, Xinchu
2017-12-01
Quarantine strategies are frequently used to control or reduce the transmission risks of epidemic diseases such as SARS, tuberculosis and cholera. In this paper, we formulate a susceptible-exposed-infected-quarantined-recovered model on a scale-free network incorporating the births and deaths of individuals. Considering that the infectivity is related to the degrees of infectious nodes, we introduce quarantined rate as a function of degree into the model, and quantify the basic reproduction number, which is shown to be dependent on some parameters, such as quarantined rate, infectivity and network structures. A theoretical result further indicates the heterogeneity of networks and higher infectivity will raise the disease transmission risk while quarantine measure will contribute to the prevention of epidemic spreading. Meanwhile, the contact assumption between susceptibles and infectives may impact the disease transmission. Furthermore, we prove that the basic reproduction number serves as a threshold value for the global stability of the disease-free and endemic equilibria and the uniform persistence of the disease on the network by constructing appropriate Lyapunov functions. Finally, some numerical simulations are illustrated to perform and complement our analytical results.
Modeling the effect of transient populations on epidemics in Washington DC.
Parikh, Nidhi; Youssef, Mina; Swarup, Samarth; Eubank, Stephen
2013-11-06
Large numbers of transients visit big cities, where they come into contact with many people at crowded areas. However, epidemiological studies have not paid much attention to the role of this subpopulation in disease spread. We evaluate the effect of transients on epidemics by extending a synthetic population model for the Washington DC metro area to include leisure and business travelers. A synthetic population is obtained by combining multiple data sources to build a detailed minute-by-minute simulation of population interaction resulting in a contact network. We simulate an influenza-like illness over the contact network to evaluate the effects of transients on the number of infected residents. We find that there are significantly more infections when transients are considered. Since much population mixing happens at major tourism locations, we evaluate two targeted interventions: closing museums and promoting healthy behavior (such as the use of hand sanitizers, covering coughs, etc.) at museums. Surprisingly, closing museums has no beneficial effect. However, promoting healthy behavior at the museums can both reduce and delay the epidemic peak. We analytically derive the reproductive number and perform stability analysis using an ODE-based model.
Modeling the effect of transient populations on epidemics in Washington DC
Parikh, Nidhi; Youssef, Mina; Swarup, Samarth; Eubank, Stephen
2013-11-01
Large numbers of transients visit big cities, where they come into contact with many people at crowded areas. However, epidemiological studies have not paid much attention to the role of this subpopulation in disease spread. We evaluate the effect of transients on epidemics by extending a synthetic population model for the Washington DC metro area to include leisure and business travelers. A synthetic population is obtained by combining multiple data sources to build a detailed minute-by-minute simulation of population interaction resulting in a contact network. We simulate an influenza-like illness over the contact network to evaluate the effects of transients on the number of infected residents. We find that there are significantly more infections when transients are considered. Since much population mixing happens at major tourism locations, we evaluate two targeted interventions: closing museums and promoting healthy behavior (such as the use of hand sanitizers, covering coughs, etc.) at museums. Surprisingly, closing museums has no beneficial effect. However, promoting healthy behavior at the museums can both reduce and delay the epidemic peak. We analytically derive the reproductive number and perform stability analysis using an ODE-based model.
Kwon, Sungchul; Kim, Yup
2013-01-01
We investigate epidemic spreading in annealed directed scale-free networks with the in-degree (k) distribution P(in)(k)~k(-γ(in)) and the out-degree (ℓ) distribution, P(out)(ℓ)~ℓ(-γ(out)). The correlation of each node on the networks is controlled by the probability r(0≤r≤1) in two different algorithms, the so-called k and ℓ algorithms. For r=1, the k algorithm gives =, whereas the ℓ algorithm gives =. For r=0, = for both algorithms. As the prototype of epidemic spreading, the susceptible-infected-susceptible model and contact process on the networks are analyzed using the heterogeneous mean-field theory and Monte Carlo simulations. The directedness of links and the correlation of the network are found to play important roles in the spreading, so that critical behaviors of both models are distinct from those on undirected scale-free networks.
Epidemics and rumours in complex networks
Draief, Moez
2009-01-01
Information propagation through peer-to-peer systems, online social systems, wireless mobile ad hoc networks and other modern structures can be modelled as an epidemic on a network of contacts. Understanding how epidemic processes interact with network topology allows us to predict ultimate course, understand phase transitions and develop strategies to control and optimise dissemination. This book is a concise introduction for applied mathematicians and computer scientists to basic models, analytical tools and mathematical and algorithmic results. Mathematical tools introduced include coupling
Susceptible-infected-recovered epidemics in random networks with population awareness
Wu, Qingchu; Chen, Shufang
2017-10-01
The influence of epidemic information-based awareness on the spread of infectious diseases on networks cannot be ignored. Within the effective degree modeling framework, we discuss the susceptible-infected-recovered model in complex networks with general awareness and general degree distribution. By performing the linear stability analysis, the conditions of epidemic outbreak can be deduced and the results of the previous research can be further expanded. Results show that the local awareness can suppress significantly the epidemic spreading on complex networks via raising the epidemic threshold and such effects are closely related to the formulation of awareness functions. In addition, our results suggest that the recovered information-based awareness has no effect on the critical condition of epidemic outbreak.
Environmental Factors Influencing Epidemic Cholera
Jutla, Antarpreet; Whitcombe, Elizabeth; Hasan, Nur; Haley, Bradd; Akanda, Ali; Huq, Anwar; Alam, Munir; Sack, R. Bradley; Colwell, Rita
2013-01-01
Cholera outbreak following the earthquake of 2010 in Haiti has reaffirmed that the disease is a major public health threat. Vibrio cholerae is autochthonous to aquatic environment, hence, it cannot be eradicated but hydroclimatology-based prediction and prevention is an achievable goal. Using data from the 1800s, we describe uniqueness in seasonality and mechanism of occurrence of cholera in the epidemic regions of Asia and Latin America. Epidemic regions are located near regional rivers and are characterized by sporadic outbreaks, which are likely to be initiated during episodes of prevailing warm air temperature with low river flows, creating favorable environmental conditions for growth of cholera bacteria. Heavy rainfall, through inundation or breakdown of sanitary infrastructure, accelerates interaction between contaminated water and human activities, resulting in an epidemic. This causal mechanism is markedly different from endemic cholera where tidal intrusion of seawater carrying bacteria from estuary to inland regions, results in outbreaks. PMID:23897993
The First Smallpox Epidemic on the Canadian Plains: In the Fur-traders' Words
Directory of Open Access Journals (Sweden)
C Stuart Houston
2000-01-01
Full Text Available William Tomison, in charge of the Hudson's Bay Company's Cumberland House on the Saskatchewan River, described the devastating smallpox epidemic of 1781 and 1782. He understood contagion, practised isolation and disinfection, and provided mortality statistics during a 'virgin soil' epidemic. Above all, he showed remarkable compassion. He and his men took dying Indians into their already crowded quarters, and provided them with food, shelter and 24 h care. This article describes the epidemic and its aftermath.
Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps
Ge, Qing; Ji, Guilin; Xu, Jiabo; Fan, Xiaolin
2016-11-01
In this paper, Brownian motion and L e ´ vy jumps are introduced to a SIS type epidemic model with nonlinear incidence rate. The dynamical behavior of the considered model is investigated. In order to reveal the extinction and permanence of the disease, two threshold values R˜0 ,R¯0 are showed. We find that if R˜0 1, the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results.
Assessment of yellow fever epidemic risk: an original multi-criteria modeling approach.
Directory of Open Access Journals (Sweden)
Sylvie Briand
Full Text Available BACKGROUND: Yellow fever (YF virtually disappeared in francophone West African countries as a result of YF mass vaccination campaigns carried out between 1940 and 1953. However, because of the failure to continue mass vaccination campaigns, a resurgence of the deadly disease in many African countries began in the early 1980s. We developed an original modeling approach to assess YF epidemic risk (vulnerability and to prioritize the populations to be vaccinated. METHODS AND FINDINGS: We chose a two-step assessment of vulnerability at district level consisting of a quantitative and qualitative assessment per country. Quantitative assessment starts with data collection on six risk factors: five risk factors associated with "exposure" to virus/vector and one with "susceptibility" of a district to YF epidemics. The multiple correspondence analysis (MCA modeling method was specifically adapted to reduce the five exposure variables to one aggregated exposure indicator. Health districts were then projected onto a two-dimensional graph to define different levels of vulnerability. Districts are presented on risk maps for qualitative analysis in consensus groups, allowing the addition of factors, such as population migrations or vector density, that could not be included in MCA. The example of rural districts in Burkina Faso show five distinct clusters of risk profiles. Based on this assessment, 32 of 55 districts comprising over 7 million people were prioritized for preventive vaccination campaigns. CONCLUSION: This assessment of yellow fever epidemic risk at the district level includes MCA modeling and consensus group modification. MCA provides a standardized way to reduce complexity. It supports an informed public health decision-making process that empowers local stakeholders through the consensus group. This original approach can be applied to any disease with documented risk factors.
The epidemic of Tuberculosis on vaccinated population
Syahrini, Intan; Sriwahyuni; Halfiani, Vera; Meurah Yuni, Syarifah; Iskandar, Taufiq; Rasudin; Ramli, Marwan
2017-09-01
Tuberculosis is an infectious disease which has caused a large number of mortality in Indonesia. This disease is caused by Mycrobacterium tuberculosis. Besides affecting lung, this disease also affects other organs such as lymph gland, intestine, kidneys, uterus, bone, and brain. This article discusses the epidemic of tuberculosis through employing the SEIR model. Here, the population is divided into four compartments which are susceptible, exposed, infected and recovered. The susceptible population is further grouped into two which are vaccinated group and unvaccinated group. The behavior of the epidemic is investigated through analysing the equilibrium of the model. The result shows that administering vaccine to the susceptible population contributes to the reduction of the tuberculosis epidemic rate.
From public outrage to the burst of public violence: An epidemic-like model
Nizamani, Sarwat; Memon, Nasrullah; Galam, Serge
2014-12-01
This study extends classical models of spreading epidemics to describe the phenomenon of contagious public outrage, which eventually leads to the spread of violence following a disclosure of some unpopular political decisions and/or activity. Accordingly, a mathematical model is proposed to simulate from the start, the internal dynamics by which an external event is turned into internal violence within a population. Five kinds of agents are considered: “Upset” (U), “Violent” (V), “Sensitive” (S), “Immune” (I), and “Relaxed” (R), leading to a set of ordinary differential equations, which in turn yield the dynamics of spreading of each type of agents among the population. The process is stopped with the deactivation of the associated issue. Conditions coinciding with a twofold spreading of public violence are singled out. The results shed new light to understand terror activity and provides some hint on how to curb the spreading of violence within population globally sensitive to specific world issues. Recent violent events in the world are discussed.
Stemming the obesity epidemic : a tantalizing prospect
Veerman, J Lennert; Barendregt, Jan J; van Beeck, Ed F; Seidell, Jacob C; Mackenbach, Johan P
OBJECTIVE: Obesity is a growing problem worldwide, but there are no good methods to assess the future course of the epidemic and the potential influence of interventions. We explore the behavior change needed to stop the obesity epidemic in the U.S. RESEARCH METHODS AND PROCEDURES: We modeled the
Could the Recent Zika Epidemic Have Been Predicted?
Vecchi, G. A.; Munoz, A. G.; Thomson, M. C.; Stewart-Ibarra, A. M.; Chourio, X.; Nájera, P.; Moran, Z.; Yang, X.
2017-12-01
Given knowledge at the time, the recent 2015-2016 zika virus (ZIKV) epidemic probably could not have been predicted. Without the prior knowledge of ZIKV being already present in South America, and given the lack of understanding of key epidemiologic processes and long-term records of ZIKV cases in the continent, the best related prediction could be carried out for the potential risk of a generic Aedes-borne disease epidemic. Here we use a recently published two-vector basic reproduction number model to assess the predictability of the conditions conducive to epidemics of diseases like zika, chikungunya, or dengue, transmitted by the independent or concurrent presence of Aedes aegypti and Aedes albopictus. We compare the potential risk of transmission forcing the model with the observed climate and with state-of-the-art operational forecasts from the North American Multi Model Ensemble (NMME), finding that the predictive skill of this new seasonal forecast system is highest for multiple countries in Latin America and the Caribbean during the December-February and March-May seasons, and slightly lower—but still of potential use to decision-makers—for the rest of the year. In particular, we find that above-normal suitable conditions for the occurrence of the zika epidemic at the beginning of 2015 could have been successfully predicted at least 1 month in advance for several zika hotspots, and in particular for Northeast Brazil: the heart of the epidemic. Nonetheless, the initiation and spread of an epidemic depends on the effect of multiple factors beyond climate conditions, and thus this type of approach must be considered as a guide and not as a formal predictive tool of vector-borne epidemics.
Research Spotlight: Model suggests path to ending the ongoing Haitian cholera epidemic
Schultz, Colin
2011-05-01
Since early November 2010 a deadly cholera epidemic has been spreading across the Caribbean nation of Haiti, killing thousands of people and infecting hundreds of thousands. While infection rates are being actively monitored, health organizations have been left without a clear understanding of exactly how the disease has spread across Haiti. Cholera can spread through exposure to contaminated water, and the disease travels over long distances if an infected individual moves around the country. Using representations of these two predominant dispersion mechanisms, along with information on the size of the susceptible population, the number of infected individuals, and the aquatic concentration of the cholera-causing bacteria for more than 500 communities, Bertuzzo et al. designed a model that was able to accurately reproduce the progression of the Haitian cholera epidemic. (Geophysical Research Letters, doi:10.1029/2011GL046823, 2011)
Dynamics of epidemics outbreaks in heterogeneous populations
Brockmann, Dirk; Morales-Gallardo, Alejandro; Geisel, Theo
2007-03-01
The dynamics of epidemic outbreaks have been investigated in recent years within two alternative theoretical paradigms. The key parameter of mean field type of models such as the SIR model is the basic reproduction number R0, the average number of secondary infections caused by one infected individual. Recently, scale free network models have received much attention as they account for the high variability in the number of social contacts involved. These models predict an infinite basic reproduction number in some cases. We investigate the impact of heterogeneities of contact rates in a generic model for epidemic outbreaks. We present a system in which both the time periods of being infectious and the time periods between transmissions are Poissonian processes. The heterogeneities are introduced by means of strongly variable contact rates. In contrast to scale free network models we observe a finite basic reproduction number and, counterintuitively a smaller overall epidemic outbreak as compared to the homogeneous system. Our study thus reveals that heterogeneities in contact rates do not necessarily facilitate the spread to infectious disease but may well attenuate it.
Blower, Sally; Go, Myong-Hyun
2011-07-19
Mathematical models are useful tools for understanding and predicting epidemics. A recent innovative modeling study by Stehle and colleagues addressed the issue of how complex models need to be to ensure accuracy. The authors collected data on face-to-face contacts during a two-day conference. They then constructed a series of dynamic social contact networks, each of which was used to model an epidemic generated by a fast-spreading airborne pathogen. Intriguingly, Stehle and colleagues found that increasing model complexity did not always increase accuracy. Specifically, the most detailed contact network and a simplified version of this network generated very similar results. These results are extremely interesting and require further exploration to determine their generalizability.
Stability analysis of the Euler discretization for SIR epidemic model
International Nuclear Information System (INIS)
Suryanto, Agus
2014-01-01
In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaos phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart
Dynamical processes and epidemic threshold on nonlinear coupled multiplex networks
Gao, Chao; Tang, Shaoting; Li, Weihua; Yang, Yaqian; Zheng, Zhiming
2018-04-01
Recently, the interplay between epidemic spreading and awareness diffusion has aroused the interest of many researchers, who have studied models mainly based on linear coupling relations between information and epidemic layers. However, in real-world networks the relation between two layers may be closely correlated with the property of individual nodes and exhibits nonlinear dynamical features. Here we propose a nonlinear coupled information-epidemic model (I-E model) and present a comprehensive analysis in a more generalized scenario where the upload rate differs from node to node, deletion rate varies between susceptible and infected states, and infection rate changes between unaware and aware states. In particular, we develop a theoretical framework of the intra- and inter-layer dynamical processes with a microscopic Markov chain approach (MMCA), and derive an analytic epidemic threshold. Our results suggest that the change of upload and deletion rate has little effect on the diffusion dynamics in the epidemic layer.
Directory of Open Access Journals (Sweden)
Mohammad Tavakolizade Ravari
2016-12-01
Full Text Available The current research aims at studying the epidemic model of the term RFID within the classes of patents. Methodology: The research is descriptive and has been conducted based on the mathematical models of diseases. Research population consists of 35,627 granted patents from the USPTO database those which the terms RFID or Radio Frequency Identification occur in their titles or abstracts. Data analysis was performed through software like Excel, SPSS, and Ravar-Matrix. Findings show that the cumulative growth of sub-classes with the term RFID follows an S-logistic model. This is an evidence of natural growth rate for assigning the term RFID to the USPTO sub-classes over the years. Other finding reveals that the term RFID has been entered into and exited from the sub-classes of patents like the SIS epidemic model of diseases. As a final conclusion, the most technical fields those that are susceptible for RFID technology, have been met this technology. On the base of SIS model, the epidemic of RFID technology has been reached a balance.
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Nishiura Hiroshi
2011-02-01
Full Text Available Abstract Background Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. Methods A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009 in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. Results The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Conclusions Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.
Impact of clinical surveillance during a foot-and-mouth disease epidemic
DEFF Research Database (Denmark)
Hisham Beshara Halasa, Tariq; Boklund, Anette
duration, number of infected herds and the economic losses from an epidemic. The stochastic spatial simulation model DTU-DADS was enhanced to include simulation of surveillance of herds within the protection and surveillance zones and the model was used to model spread of FMD between herds. A queuing......The objectives of this study were to assess, whether the current surveillance capacity is sufficient to fulfill EU and Danish regulations to control a hypothetical foot-and-mouth disease (FMD) epidemic in Denmark, and whether enlarging the protection and/or surveillance zones could reduce epidemic...... showed that the default surveillance capacity is sufficient to survey herds within one week of the zones establishment, as the regulations demand. Extra resources for surveillance did not reduce the costs of the epidemics, but fewer resources could result in larger epidemics and costs. Furthermore...
Fan, Kuangang; Zhang, Yan; Gao, Shujing; Wei, Xiang
2017-09-01
A class of SIR epidemic model with generalized nonlinear incidence rate is presented in this paper. Temporary immunity and stochastic perturbation are also considered. The existence and uniqueness of the global positive solution is achieved. Sufficient conditions guaranteeing the extinction and persistence of the epidemic disease are established. Moreover, the threshold behavior is discussed, and the threshold value R0 is obtained. We show that if R0 extinct with probability one, whereas if R0 > 1, then the system remains permanent in the mean.
Christakos, G.; Olea, R.A.; Yu, H.-L.
2007-01-01
Background: This work demonstrates the importance of spatiotemporal stochastic modelling in constructing maps of major epidemics from fragmentary information, assessing population impacts, searching for possible etiologies, and performing comparative analysis of epidemics. Methods: Based on the theory previously published by the authors and incorporating new knowledge bases, informative maps of the composite space-time distributions were generated for important characteristics of two major epidemics: Black Death (14th century Western Europe) and bubonic plague (19th-20th century Indian subcontinent). Results: The comparative spatiotemporal analysis of the epidemics led to a number of interesting findings: (1) the two epidemics exhibited certain differences in their spatiotemporal characteristics (correlation structures, trends, occurrence patterns and propagation speeds) that need to be explained by means of an interdisciplinary effort; (2) geographical epidemic indicators confirmed in a rigorous quantitative manner the partial findings of isolated reports and time series that Black Death mortality was two orders of magnitude higher than that of bubonic plague; (3) modern bubonic plague is a rural disease hitting harder the small villages in the countryside whereas Black Death was a devastating epidemic that indiscriminately attacked large urban centres and the countryside, and while the epidemic in India lasted uninterruptedly for five decades, in Western Europe it lasted three and a half years; (4) the epidemics had reverse areal extension features in response to annual seasonal variations. Temperature increase at the end of winter led to an expansion of infected geographical area for Black Death and a reduction for bubonic plague, reaching a climax at the end of spring when the infected area in Western Europe was always larger than in India. Conversely, without exception, the infected area during winter was larger for the Indian bubonic plague; (5) during the
A micro-epidemic model for primary dengue infection
Mishra, Arti; Gakkhar, Sunita
2017-06-01
In this paper, a micro-epidemic non-linear dynamical model has been proposed and analyzed for primary dengue infection. The model incorporates the effects of T cells immune response as well as humoral response during pathogenesis of dengue infection. The time delay has been accounted for production of antibodies from B cells. The basic reproduction number (R0) has been computed. Three equilibrium states are obtained. The existence and stability conditions for infection-free and ineffective cellular immune response state have been discussed. The conditions for existence of endemic state have been obtained. Further, the parametric region is obtained where system exhibits complex behavior. The threshold value of time delay has been computed which is critical for change in stability of endemic state. A threshold level for antibodies production rate has been obtained over which the infection will die out even though R0 > 1. The model is in line with the clinical observation that viral load decreases within 7-14 days from the onset of primary infection.
Epidemic Intelligence. Langmuir and the Birth of Disease Surveillance
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Lyle Fearnley
2010-12-01
Full Text Available In the wake of the SARS and influenza epidemics of the past decade, one public health solution has become a refrain: surveillance systems for detection of disease outbreaks. This paper is an effort to understand how disease surveillance for outbreak detection gained such paramount rationality in contemporary public health. The epidemiologist Alexander Langmuir is well known as the creator of modern disease surveillance. But less well known is how he imagined disease surveillance as one part of what he called “epidemic intelligence.” Langmuir developed the practice of disease surveillance during an unprecedented moment in which the threat of biological warfare brought civil defense experts and epidemiologists together around a common problem. In this paper, I describe how Langmuir navigated this world, experimenting with new techniques and rationales of epidemic control. Ultimately, I argue, Langmuir′s experiments resulted in a set of techniques and infrastructures – a system of epidemic intelligence – that transformed the epidemic as an object of human art.
On The Travelling Wave Solution For An SEIR Epidemic Disease ...
African Journals Online (AJOL)
We present the travelling wave solution for a Susceptible, Exposed, Infective and Removed (SEIR) epidemic disease model. For this SEIR model, the disease is driven by both the latent and infective class (the diffusion term is included in both classes). The population is closed. Keywords: Epidemic model, spatial spread, ...
Could the Recent Zika Epidemic Have Been Predicted?
Directory of Open Access Journals (Sweden)
Ángel G. Muñoz
2017-07-01
Full Text Available Given knowledge at the time, the recent 2015–2016 zika virus (ZIKV epidemic probably could not have been predicted. Without the prior knowledge of ZIKV being already present in South America, and given the lack of understanding of key epidemiologic processes and long-term records of ZIKV cases in the continent, the best related prediction could be carried out for the potential risk of a generic Aedes-borne disease epidemic. Here we use a recently published two-vector basic reproduction number model to assess the predictability of the conditions conducive to epidemics of diseases like zika, chikungunya, or dengue, transmitted by the independent or concurrent presence of Aedes aegypti and Aedes albopictus. We compare the potential risk of transmission forcing the model with the observed climate and with state-of-the-art operational forecasts from the North American Multi Model Ensemble (NMME, finding that the predictive skill of this new seasonal forecast system is highest for multiple countries in Latin America and the Caribbean during the December-February and March-May seasons, and slightly lower—but still of potential use to decision-makers—for the rest of the year. In particular, we find that above-normal suitable conditions for the occurrence of the zika epidemic at the beginning of 2015 could have been successfully predicted at least 1 month in advance for several zika hotspots, and in particular for Northeast Brazil: the heart of the epidemic. Nonetheless, the initiation and spread of an epidemic depends on the effect of multiple factors beyond climate conditions, and thus this type of approach must be considered as a guide and not as a formal predictive tool of vector-borne epidemics.
[Hippocrates. Aphorisms and Epidemics III. Two clinical texts].
Frøland, Anders
2015-01-01
The two Hippocratic texts, Aphorisms and Epidemics III, have not been translated into Danish previously. The Aphorisms are 412 short, pithy statements, mostly on the prognosis in relation to certain symptoms in the course of the diseases, very often febrile. The Aphorisms begin with the famous words: "Life is short, the Art long, opportunity fleeting, experiment treacherous, judgment difficult." (Transl. W H S Jones [22]). Epidemics III consists of 28 case histories, again mostly of febrile patients, but also of observations on the connection of the seasons with general morbidity and mortality. The author describes an epidemic, which in some respects resembles Thucydides' report on the plague in Athens in 430 BC. It is suggested, that observations as have been recorded in the seven Hippocratic texts on epidemic diseases are the material on which prognostic statements as those collected in the Aphorisms are founded.
Epidemic dynamics and endemic states in complex networks
Pastor-Satorras, Romualdo; Vespignani, Alessandro
2001-01-01
We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. In networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below which the infection prevalence is null. On the contrary, on a wide range of scale-free networks we observe the absence of an epidemic threshold and its associated critical behavior. This implies that scale-free networks are pron...
2011-01-01
Background Simulation models of influenza spread play an important role for pandemic preparedness. However, as the world has not faced a severe pandemic for decades, except the rather mild H1N1 one in 2009, pandemic influenza models are inherently hypothetical and validation is, thus, difficult. We aim at reconstructing a recent seasonal influenza epidemic that occurred in Switzerland and deem this to be a promising validation strategy for models of influenza spread. Methods We present a spatially explicit, individual-based simulation model of influenza spread. The simulation model bases upon (i) simulated human travel data, (ii) data on human contact patterns and (iii) empirical knowledge on the epidemiology of influenza. For model validation we compare the simulation outcomes with empirical knowledge regarding (i) the shape of the epidemic curve, overall infection rate and reproduction number, (ii) age-dependent infection rates and time of infection, (iii) spatial patterns. Results The simulation model is capable of reproducing the shape of the 2003/2004 H3N2 epidemic curve of Switzerland and generates an overall infection rate (14.9 percent) and reproduction numbers (between 1.2 and 1.3), which are realistic for seasonal influenza epidemics. Age and spatial patterns observed in empirical data are also reflected by the model: Highest infection rates are in children between 5 and 14 and the disease spreads along the main transport axes from west to east. Conclusions We show that finding evidence for the validity of simulation models of influenza spread by challenging them with seasonal influenza outbreak data is possible and promising. Simulation models for pandemic spread gain more credibility if they are able to reproduce seasonal influenza outbreaks. For more robust modelling of seasonal influenza, serological data complementing sentinel information would be beneficial. PMID:21554680
[Scabies epidemic in a sheltered workshop--what should be done?].
Mayer, J; Wever, S; Lurz, C; Bröcker, E B
2000-02-01
Scabies is an infectious parasitic skin disease with a notable rising incidence in Germany. The disease is usually transmitted by close physical contact, but indirect spread e.g. by bedding is also possible. Due to its contagiousness, introduction of scabies into crowding living facilities, such as dormitories or kindergartens, can easily cause an epidemic outbreak. We describe an epidemic of scabies in a workshop for handicapped people in February 1998. A worker with severe scabies reported that numerous colleagues in both workshop and the associated hostel had complained of pruritus for months and that some of them already had undergone scabicide treatment. The number of contacts (staff, colleagues, friends, attendants, family) of our patient and the other already affected people was more than 460. The management of the workshop asked for help in handling the epidemic. We describe the cooperative efforts of the management, as well as hospital and private dermatologists, to evaluate all potential contacts and present a concept of treatment for the termination of such an epidemic outbreak of scabies.
Hybrid epidemics--a case study on computer worm conficker.
Directory of Open Access Journals (Sweden)
Changwang Zhang
Full Text Available Conficker is a computer worm that erupted on the Internet in 2008. It is unique in combining three different spreading strategies: local probing, neighbourhood probing, and global probing. We propose a mathematical model that combines three modes of spreading: local, neighbourhood, and global, to capture the worm's spreading behaviour. The parameters of the model are inferred directly from network data obtained during the first day of the Conficker epidemic. The model is then used to explore the tradeoff between spreading modes in determining the worm's effectiveness. Our results show that the Conficker epidemic is an example of a critically hybrid epidemic, in which the different modes of spreading in isolation do not lead to successful epidemics. Such hybrid spreading strategies may be used beneficially to provide the most effective strategies for promulgating information across a large population. When used maliciously, however, they can present a dangerous challenge to current internet security protocols.
Hybrid epidemics--a case study on computer worm conficker.
Zhang, Changwang; Zhou, Shi; Chain, Benjamin M
2015-01-01
Conficker is a computer worm that erupted on the Internet in 2008. It is unique in combining three different spreading strategies: local probing, neighbourhood probing, and global probing. We propose a mathematical model that combines three modes of spreading: local, neighbourhood, and global, to capture the worm's spreading behaviour. The parameters of the model are inferred directly from network data obtained during the first day of the Conficker epidemic. The model is then used to explore the tradeoff between spreading modes in determining the worm's effectiveness. Our results show that the Conficker epidemic is an example of a critically hybrid epidemic, in which the different modes of spreading in isolation do not lead to successful epidemics. Such hybrid spreading strategies may be used beneficially to provide the most effective strategies for promulgating information across a large population. When used maliciously, however, they can present a dangerous challenge to current internet security protocols.
Disease-induced resource constraints can trigger explosive epidemics
Böttcher, L.; Woolley-Meza, O.; Araújo, N. A. M.; Herrmann, H. J.; Helbing, D.
2015-11-01
Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into “explosive” spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process.
Concurrency-Induced Transitions in Epidemic Dynamics on Temporal Networks.
Onaga, Tomokatsu; Gleeson, James P; Masuda, Naoki
2017-09-08
Social contact networks underlying epidemic processes in humans and animals are highly dynamic. The spreading of infections on such temporal networks can differ dramatically from spreading on static networks. We theoretically investigate the effects of concurrency, the number of neighbors that a node has at a given time point, on the epidemic threshold in the stochastic susceptible-infected-susceptible dynamics on temporal network models. We show that network dynamics can suppress epidemics (i.e., yield a higher epidemic threshold) when the node's concurrency is low, but can also enhance epidemics when the concurrency is high. We analytically determine different phases of this concurrency-induced transition, and confirm our results with numerical simulations.
Concurrency-Induced Transitions in Epidemic Dynamics on Temporal Networks
Onaga, Tomokatsu; Gleeson, James P.; Masuda, Naoki
2017-09-01
Social contact networks underlying epidemic processes in humans and animals are highly dynamic. The spreading of infections on such temporal networks can differ dramatically from spreading on static networks. We theoretically investigate the effects of concurrency, the number of neighbors that a node has at a given time point, on the epidemic threshold in the stochastic susceptible-infected-susceptible dynamics on temporal network models. We show that network dynamics can suppress epidemics (i.e., yield a higher epidemic threshold) when the node's concurrency is low, but can also enhance epidemics when the concurrency is high. We analytically determine different phases of this concurrency-induced transition, and confirm our results with numerical simulations.
The Global Behavior of a Periodic Epidemic Model with Travel between Patches
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Luosheng Wen
2012-01-01
Full Text Available We establish an SIS (susceptible-infected-susceptible epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratio R0 and two theorems on the global behavior: if R0 1, then it is unstable; if R0 > 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.
Dynamic behavior of the interaction between epidemics and cascades on heterogeneous networks
Jiang, Lurong; Jin, Xinyu; Xia, Yongxiang; Ouyang, Bo; Wu, Duanpo
2014-12-01
Epidemic spreading and cascading failure are two important dynamical processes on complex networks. They have been investigated separately for a long time. But in the real world, these two dynamics sometimes may interact with each other. In this paper, we explore a model combined with the SIR epidemic spreading model and a local load sharing cascading failure model. There exists a critical value of the tolerance parameter for which the epidemic with high infection probability can spread out and infect a fraction of the network in this model. When the tolerance parameter is smaller than the critical value, the cascading failure cuts off the abundance of paths and blocks the spreading of the epidemic locally. While the tolerance parameter is larger than the critical value, the epidemic spreads out and infects a fraction of the network. A method for estimating the critical value is proposed. In simulations, we verify the effectiveness of this method in the uncorrelated configuration model (UCM) scale-free networks.
Frasca, Mattia; Sharkey, Kieran J
2016-06-21
Understanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible-infectious-removed) dynamics propagated on contact networks. We derive a novel set of 'discrete-time moment equations' for the probability of the system states at the level of individual nodes and pairs of nodes. These equations form a set which we close by introducing appropriate approximations of the joint probabilities appearing in them. For the example case of SIR processes, we formulate two types of model, one assuming statistical independence at the level of individuals and one at the level of pairs. From the pair-based model we then derive a model at the level of the population which captures the behavior of epidemics on homogeneous random networks. With respect to their continuous-time counterparts, the models include a larger number of possible transitions from one state to another and joint probabilities with a larger number of individuals. The approach is validated through numerical simulation over different network topologies. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.
Toward a generalized theory of epidemic awareness in social networks
Wu, Qingchu; Zhu, Wenfang
We discuss the dynamics of a susceptible-infected-susceptible (SIS) model with local awareness in networks. Individual awareness to the infectious disease is characterized by a general function of epidemic information in its neighborhood. We build a high-accuracy approximate equation governing the spreading dynamics and derive an approximate epidemic threshold above which the epidemic spreads over the whole network. Our results extend the previous work and show that the epidemic threshold is dependent on the awareness function in terms of one infectious neighbor. Interestingly, when a pow-law awareness function is chosen, the epidemic threshold can emerge in infinite networks.
Directory of Open Access Journals (Sweden)
Worapol Aengwanich
2014-04-01
Full Text Available Thailand is located in Southeast Asia and is a country that was affected by highly pathogenic avian influenza (HPAI epidemics during 2003–2004. Nevertheless, the Thai government’s issuance policy of strict control and prevention of the disease has resulted in efficient disease control of avian influenza (AI. Poultry farmers have been both positively and negatively affected by this policy. There are three poultry cluster models worthy of attention in Thailand: (1 egg chicken poultry clusters over ponds; (2 egg chicken poultry clusters in coops raised from the ground and managed by a cooperative; and (3 poultry clusters in closed coops under contract with the private sector. Following the AI epidemics, additional poultry husbandry and biosecurity systems were developed, thereby generating income and improving the quality of life for poultry farmers. Nevertheless, raising large clusters of poultry in the same area results in disadvantages, particularly problems with both air and water pollution, depending upon the environments of each poultry model. Furthermore, the government’s policy for controlling AI during epidemics has had a negative effect on the relationship between officials and farmers, due to poultry destruction measures.
Study on the Occurrence and Epidemic Model of Rape Sclerotinia Stem Rot of ‘Zheyou 50’
Xu Sen-fu; Wang Hui-fu; Yu Shanhong; Wang En-guo
2013-01-01
In order to investigate invading and epidemic rules of rape sclerotinia stem rot of ‘Zheyou 50’ and promote the development of brassica campestris industry, this paper studied the outbreak regularity and epidemic model of rape sclerotinia stem rot according to field investigation and infection. The result showed that machinery direct seeding rape was good for the occurrence of sclerotinia stem rot for the reason of late seeding and high density. The period from water damage appeared to wiltin...
Yokota, Masashi; Watanabe, Seiichi; Hatai, Kishio; Kurata, Osamu; Furihata, Mituru; Usui, Takahiko
2008-12-01
The epidemic process of the parasite Ichthyophonus hoferi in cultured rainbow trout Oncorhynchus mykiss was quantitatively estimated by both the cohabitation experiment and two standard models (the Kermarck-McKendrick model and the Reed-Frost model). For analysis of the parasite transmission by cohabitation, fish in two replicate tanks were exposed to 1, 5, or 10 infected fish, and daily mortality was counted for 102 d. Despite simple experiments for artificial exposure to the pathogen, the daily estimate of dead fish in the Kermarck-McKendrick model did not fit the observed number of dead fish in the experiment. In contrast, when the longest possible incubation period (generation time) was assumed to be 51 d in the Reed-Frost model, the estimated number of dead fish in discrete generations was close to the observed number of dead fish. If the time unit was 51 d, the estimated mortalities in the generation-based Kermarck-McKendrick model were significantly correlated with observed mortalities. These results suggest that the deterministic aspects of the epidemic process of the parasite can be quantitatively demonstrated on a 51-d timescale or longer, whereas transmission on a daily timescale is uncertain.
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Go Myong-Hyun
2011-07-01
Full Text Available Abstract Mathematical models are useful tools for understanding and predicting epidemics. A recent innovative modeling study by Stehle and colleagues addressed the issue of how complex models need to be to ensure accuracy. The authors collected data on face-to-face contacts during a two-day conference. They then constructed a series of dynamic social contact networks, each of which was used to model an epidemic generated by a fast-spreading airborne pathogen. Intriguingly, Stehle and colleagues found that increasing model complexity did not always increase accuracy. Specifically, the most detailed contact network and a simplified version of this network generated very similar results. These results are extremely interesting and require further exploration to determine their generalizability. Please see related article BMC Medicine, 2011, 9:87
Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination
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Lei Wang
2017-01-01
Full Text Available In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed.
the south african hiv epidemic, reflected by nine provincial ...
African Journals Online (AJOL)
the distribution and trend of the HIV epidemic in each of the ... The exponential model significantly explains the HIV epidemics in the .... such a curve is considered to be made up of three. October 199 ..... Ut: Quantitative Forecasting Methods.
Epidemic spreading on preferred degree adaptive networks.
Jolad, Shivakumar; Liu, Wenjia; Schmittmann, B; Zia, R K P
2012-01-01
We study the standard SIS model of epidemic spreading on networks where individuals have a fluctuating number of connections around a preferred degree κ. Using very simple rules for forming such preferred degree networks, we find some unusual statistical properties not found in familiar Erdös-Rényi or scale free networks. By letting κ depend on the fraction of infected individuals, we model the behavioral changes in response to how the extent of the epidemic is perceived. In our models, the behavioral adaptations can be either 'blind' or 'selective'--depending on whether a node adapts by cutting or adding links to randomly chosen partners or selectively, based on the state of the partner. For a frozen preferred network, we find that the infection threshold follows the heterogeneous mean field result λ(c)/μ = / and the phase diagram matches the predictions of the annealed adjacency matrix (AAM) approach. With 'blind' adaptations, although the epidemic threshold remains unchanged, the infection level is substantially affected, depending on the details of the adaptation. The 'selective' adaptive SIS models are most interesting. Both the threshold and the level of infection changes, controlled not only by how the adaptations are implemented but also how often the nodes cut/add links (compared to the time scales of the epidemic spreading). A simple mean field theory is presented for the selective adaptations which capture the qualitative and some of the quantitative features of the infection phase diagram.
Epidemic spreading in scale-free networks including the effect of individual vigilance
International Nuclear Information System (INIS)
Gong Yong-Wang; Song Yu-Rong; Jiang Guo-Ping
2012-01-01
In this paper, we study the epidemic spreading in scale-free networks and propose a new susceptible-infected-recovered (SIR) model that includes the effect of individual vigilance. In our model, the effective spreading rate is dynamically adjusted with the time evolution at the vigilance period. Using the mean-field theory, an analytical result is derived. It shows that individual vigilance has no effect on the epidemic threshold. The numerical simulations agree well with the analytical result. Furthermore, we investigate the effect of individual vigilance on the epidemic spreading speed. It is shown that individual vigilance can slow the epidemic spreading speed effectively and delay the arrival of peak epidemic infection. (general)
Sabbatani, Sergio
2003-03-01
When the "Black Death" swept through Europe from southern France in 1348, in the short space of two years the Europeans were hit by one of the most serious epidemics ever recorded in human history. Yersinia pestis reached Europe by sea, its contamination propagated by the Genoese ships coming from the Crimean port of Jaffa. For the first time the world experienced microbiological unification: East and West were equally involved in the tragedy that spread, and no town remained unscathed during the various epidemic waves which succeeded one another in the following three centuries. The authors of this article describe how and why the epidemic spread, as well as the factors that led to the swift, and often fatal, involment of millions of Europeans. The second part of the article deals with the measures taken by the healthcare authorities of European towns and countries in order to halt the proliferation of the disease. According to the data and observations by authoritative authors, selected among the many who studied the disease that from the 14th century spread like a scourge throughout the known world at the time, the epidemic could have been even more serious, in terms of mortality and morbidity, without the disciplinary and provisional health measures taken. The experience gained in Italy and all over Europe at the time proved useful not only to better manage the epidemics which cyclically broke out, but also to efficiently combat the cholera epidemics of the 19th century. With the 14th century plague epidemic, the Europeans and their political and administrative representatives may well have realized for the very first time that contamination could be combatted by adopting a set of rational, scientific norms - although in practice such rules were mostly inspired by misguided scientific theories. Humankind was no longer alone. A new society was emerging, one that was not going to passively accept the more or less mysterious ways of a superior being of fate. The
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Katelyn C. Corey
2016-09-01
Full Text Available Using a mathematical model with realistic demography, we analyze a large outbreak of measles in Muyinga sector in rural Burundi in 1988–1989. We generate simulated epidemic curves and age × time epidemic surfaces, which we qualitatively and quantitatively compare with the data. Our findings suggest that supplementary immunization activities (SIAs should be used in places where routine vaccination cannot keep up with the increasing numbers of susceptible individuals resulting from population growth or from logistical problems such as cold chain maintenance. We use the model to characterize the relationship between SIA frequency and SIA age range necessary to suppress measles outbreaks. If SIAs are less frequent, they must expand their target age range.
Drought and Epidemic Typhus, Central Mexico, 1655–1918
Acuna-Soto, Rudofo; Stahle, David W.
2014-01-01
Epidemic typhus is an infectious disease caused by the bacterium Rickettsia prowazekii and transmitted by body lice (Pediculus humanus corporis). This disease occurs where conditions are crowded and unsanitary. This disease accompanied war, famine, and poverty for centuries. Historical and proxy climate data indicate that drought was a major factor in the development of typhus epidemics in Mexico during 1655–1918. Evidence was found for 22 large typhus epidemics in central Mexico, and tree-ring chronologies were used to reconstruct moisture levels over central Mexico for the past 500 years. Below-average tree growth, reconstructed drought, and low crop yields occurred during 19 of these 22 typhus epidemics. Historical documents describe how drought created large numbers of environmental refugees that fled the famine-stricken countryside for food relief in towns. These refugees often ended up in improvised shelters in which crowding encouraged conditions necessary for spread of typhus. PMID:24564928
Epidemic spread over networks with agent awareness and social distancing
Paarporn, Keith
2016-04-20
We study an SIS epidemic model over an arbitrary connected network topology when the agents receive personalized information about the current epidemic state. The agents utilize their available information to either reduce interactions with their neighbors (social distancing) when they believe the epidemic is currently prevalent or resume normal interactions when they believe there is low risk of becoming infected. The information is a weighted combination of three sources: 1) the average states of nodes in contact neighborhoods 2) the average states of nodes in an information network 3) a global broadcast of the average epidemic state of the network. A 2n-state Markov Chain is first considered to model the disease dynamics with awareness, from which a mean-field discrete-time n-state dynamical system is derived, where each state corresponds to an agent\\'s probability of being infected. The nonlinear model is a lower bound of its linearized version about the origin. Hence, global stability of the origin (the diseasefree equilibrium) in the linear model implies global stability in the nonlinear model. When the origin is not stable, we show the existence of a nontrivial fixed point in the awareness model, which obeys a strict partial order in relation to the nontrivial fixed point of the dynamics without distancing. In simulations, we define two performance metrics to understand the effectiveness agent awareness has in reducing the spread of an epidemic. © 2015 IEEE.
Epidemic outbreaks in growing scale-free networks with local structure
Ni, Shunjiang; Weng, Wenguo; Shen, Shifei; Fan, Weicheng
2008-09-01
The class of generative models has already attracted considerable interest from researchers in recent years and much expanded the original ideas described in BA model. Most of these models assume that only one node per time step joins the network. In this paper, we grow the network by adding n interconnected nodes as a local structure into the network at each time step with each new node emanating m new edges linking the node to the preexisting network by preferential attachment. This successfully generates key features observed in social networks. These include power-law degree distribution pk∼k, where μ=(n-1)/m is a tuning parameter defined as the modularity strength of the network, nontrivial clustering, assortative mixing, and modular structure. Moreover, all these features are dependent in a similar way on the parameter μ. We then study the susceptible-infected epidemics on this network with identical infectivity, and find that the initial epidemic behavior is governed by both of the infection scheme and the network structure, especially the modularity strength. The modularity of the network makes the spreading velocity much lower than that of the BA model. On the other hand, increasing the modularity strength will accelerate the propagation velocity.
A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment.
Papa, Federico; Binda, Francesca; Felici, Giovanni; Franzetti, Marco; Gandolfi, Alberto; Sinisgalli, Carmela; Balotta, Claudia
2018-02-01
In the present paper we propose a simple time-varying ODE model to describe the evolution of HIV epidemic in Italy. The model considers a single population of susceptibles, without distinction of high-risk groups within the general population, and accounts for the presence of immigration and emigration, modelling their effects on both the general demography and the dynamics of the infected subpopulations. To represent the intra-host disease progression, the untreated infected population is distributed over four compartments in cascade according to the CD4 counts. A further compartment is added to represent infected people under antiretroviral therapy. The per capita exit rate from treatment, due to voluntary interruption or failure of therapy, is assumed variable with time. The values of the model parameters not reported in the literature are assessed by fitting available epidemiological data over the decade 2003÷2012. Predictions until year 2025 are computed, enlightening the impact on the public health of the early initiation of the antiretroviral therapy. The benefits of this change in the treatment eligibility consist in reducing the HIV incidence rate, the rate of new AIDS cases, and the rate of death from AIDS. Analytical results about properties of the model in its time-invariant form are provided, in particular the global stability of the equilibrium points is established either in the absence and in the presence of infected among immigrants.
Epidemic spreading on dual-structure networks with mobile agents
Yao, Yiyang; Zhou, Yinzuo
2017-02-01
The rapid development of modern society continually transforms the social structure which leads to an increasingly distinct dual structure of higher population density in urban areas and lower density in rural areas. Such structure may induce distinctive spreading behavior of epidemics which does not happen in a single type structure. In this paper, we study the epidemic spreading of mobile agents on dual structure networks based on SIRS model. First, beyond the well known epidemic threshold for generic epidemic model that when the infection rate is below the threshold a pertinent infectious disease will die out, we find the other epidemic threshold which appears when the infection rate of a disease is relatively high. This feature of two thresholds for the SIRS model may lead to the elimination of infectious disease when social network has either high population density or low population density. Interestingly, however, we find that when a high density area is connected to a low density may cause persistent spreading of the infectious disease, even though the same disease will die out when it spreads in each single area. This phenomenon indicates the critical role of the connection between the two areas which could radically change the behavior of spreading dynamics. Our findings, therefore, provide new understanding of epidemiology pertinent to the characteristic modern social structure and have potential to develop controlling strategies accordingly.
Impact of the infectious period on epidemics
Wilkinson, Robert R.; Sharkey, Kieran J.
2018-05-01
The duration of the infectious period is a crucial determinant of the ability of an infectious disease to spread. We consider an epidemic model that is network based and non-Markovian, containing classic Kermack-McKendrick, pairwise, message passing, and spatial models as special cases. For this model, we prove a monotonic relationship between the variability of the infectious period (with fixed mean) and the probability that the infection will reach any given subset of the population by any given time. For certain families of distributions, this result implies that epidemic severity is decreasing with respect to the variance of the infectious period. The striking importance of this relationship is demonstrated numerically. We then prove, with a fixed basic reproductive ratio (R0), a monotonic relationship between the variability of the posterior transmission probability (which is a function of the infectious period) and the probability that the infection will reach any given subset of the population by any given time. Thus again, even when R0 is fixed, variability of the infectious period tends to dampen the epidemic. Numerical results illustrate this but indicate the relationship is weaker. We then show how our results apply to message passing, pairwise, and Kermack-McKendrick epidemic models, even when they are not exactly consistent with the stochastic dynamics. For Poissonian contact processes, and arbitrarily distributed infectious periods, we demonstrate how systems of delay differential equations and ordinary differential equations can provide upper and lower bounds, respectively, for the probability that any given individual has been infected by any given time.
Beretta, E; Capasso, V; Rinaldi, F
1988-01-01
The paper contains an extension of the general ODE system proposed in previous papers by the same authors, to include distributed time delays in the interaction terms. The new system describes a large class of Lotka-Volterra like population models and epidemic models with continuous time delays. Sufficient conditions for the boundedness of solutions and for the global asymptotic stability of nontrivial equilibrium solutions are given. A detailed analysis of the epidemic system is given with respect to the conditions for global stability. For a relevant subclass of these systems an existence criterion for steady states is also given.
Impacts of clustering on interacting epidemics.
Wang, Bing; Cao, Lang; Suzuki, Hideyuki; Aihara, Kazuyuki
2012-07-07
Since community structures in real networks play a major role for the epidemic spread, we therefore explore two interacting diseases spreading in networks with community structures. As a network model with community structures, we propose a random clique network model composed of different orders of cliques. We further assume that each disease spreads only through one type of cliques; this assumption corresponds to the issue that two diseases spread inside communities and outside them. Considering the relationship between the susceptible-infected-recovered (SIR) model and the bond percolation theory, we apply this theory to clique random networks under the assumption that the occupation probability is clique-type dependent, which is consistent with the observation that infection rates inside a community and outside it are different, and obtain a number of statistical properties for this model. Two interacting diseases that compete the same hosts are also investigated, which leads to a natural generalization of analyzing an arbitrary number of infectious diseases. For two-disease dynamics, the clustering effect is hypersensitive to the cohesiveness and concentration of cliques; this illustrates the impacts of clustering and the composition of subgraphs in networks on epidemic behavior. The analysis of coexistence/bistability regions provides significant insight into the relationship between the network structure and the potential epidemic prevalence. Copyright © 2012 Elsevier Ltd. All rights reserved.
(Epidemic of bacillary dysentery)
Energy Technology Data Exchange (ETDEWEB)
Auger, P.; Pouliot, B.; De Grace, M.; Milot, C.; Lafortune, M.; Bergeron, Z.
1981-10-01
An outbreak of bacillary dysentery in 1978 affecting 928 persons, most of whom were living in the village of St-Jacques, PQ, is described. An epidemiologic study suggested the water supply as the source of the infection, and it was established that the water carried by the municipal aqueduct was contaminated by feces containing the causal agent, Shigella sonnei. This epidemic, the largest mentioned in he Canadian medical literature, demonstrates how contagious this infection is.
A stochastic SIRS epidemic model with infectious force under intervention strategies
Cai, Yongli; Kang, Yun; Banerjee, Malay; Wang, Weiming
2015-12-01
In this paper, we extend a classical SIRS epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation (SDE) one through introducing random fluctuations. The value of our study lies in two aspects. Mathematically, by using the Markov semigroups theory, we prove that the reproduction number R0S can be used to govern the stochastic dynamics of SDE model. If R0S 1, under mild extra conditions, it has an endemic stationary distribution which leads to the stochastical persistence of the disease. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics.
Modelling control of epidemics spreading by long-range interactions.
Dybiec, Bartłomiej; Kleczkowski, Adam; Gilligan, Christopher A
2009-10-06
We have studied the spread of epidemics characterized by a mixture of local and non-local interactions. The infection spreads on a two-dimensional lattice with the fixed nearest neighbour connections. In addition, long-range dynamical links are formed by moving agents (vectors). Vectors perform random walks, with step length distributed according to a thick-tail distribution. Two distributions are considered in this paper, an alpha-stable distribution describing self-similar vector movement, yet characterized by an infinite variance and an exponential power characterized by a large but finite variance. Such long-range interactions are hard to track and make control of epidemics very difficult. We also allowed for cryptic infection, whereby an infected individual on the lattice can be infectious prior to showing any symptoms of infection or disease. To account for such cryptic spread, we considered a control strategy in which not only detected, i.e. symptomatic, individuals but also all individuals within a certain control neighbourhood are treated upon the detection of disease. We show that it is possible to eradicate the disease by using such purely local control measures, even in the presence of long-range jumps. In particular, we show that the success of local control and the choice of the optimal strategy depend in a non-trivial way on the dispersal patterns of the vectors. By characterizing these patterns using the stability index of the alpha-stable distribution to change the power-law behaviour or the exponent characterizing the decay of an exponential power distribution, we show that infection can be successfully contained using relatively small control neighbourhoods for two limiting cases for long-distance dispersal and for vectors that are much more limited in their dispersal range.
Evaluating Subcriticality during the Ebola Epidemic in West Africa.
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Wayne T A Enanoria
Full Text Available The 2014-2015 Ebola outbreak is the largest and most widespread to date. In order to estimate ongoing transmission in the affected countries, we estimated the weekly average number of secondary cases caused by one individual infected with Ebola throughout the infectious period for each affected West African country using a stochastic hidden Markov model fitted to case data from the World Health Organization. If the average number of infections caused by one Ebola infection is less than 1.0, the epidemic is subcritical and cannot sustain itself. The epidemics in Liberia and Sierra Leone have approached subcriticality at some point during the epidemic; the epidemic in Guinea is ongoing with no evidence that it is subcritical. Response efforts to control the epidemic should continue in order to eliminate Ebola cases in West Africa.
How heterogeneous susceptibility and recovery rates affect the spread of epidemics on networks
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Wei Gou
2017-08-01
Full Text Available In this paper, an extended heterogeneous SIR model is proposed, which generalizes the heterogeneous mean-field theory. Different from the traditional heterogeneous mean-field model only taking into account the heterogeneity of degree, our model considers not only the heterogeneity of degree but also the heterogeneity of susceptibility and recovery rates. Then, we analytically study the basic reproductive number and the final epidemic size. Combining with numerical simulations, it is found that the basic reproductive number depends on the mean of distributions of susceptibility and disease course when both of them are independent. If the mean of these two distributions is identical, increasing the variance of susceptibility may block the spread of epidemics, while the corresponding increase in the variance of disease course has little effect on the final epidemic size. It is also shown that positive correlations between individual susceptibility, course of disease and the square of degree make the population more vulnerable to epidemic and avail to the epidemic prevalence, whereas the negative correlations make the population less vulnerable and impede the epidemic prevalence. Keywords: Networks, Heterogeneity, Susceptibility, Recovery rates, Correlation, The basic reproductive number, The final epidemic size
Inferring epidemic network topology from surveillance data.
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Xiang Wan
Full Text Available The transmission of infectious diseases can be affected by many or even hidden factors, making it difficult to accurately predict when and where outbreaks may emerge. One approach at the moment is to develop and deploy surveillance systems in an effort to detect outbreaks as timely as possible. This enables policy makers to modify and implement strategies for the control of the transmission. The accumulated surveillance data including temporal, spatial, clinical, and demographic information, can provide valuable information with which to infer the underlying epidemic networks. Such networks can be quite informative and insightful as they characterize how infectious diseases transmit from one location to another. The aim of this work is to develop a computational model that allows inferences to be made regarding epidemic network topology in heterogeneous populations. We apply our model on the surveillance data from the 2009 H1N1 pandemic in Hong Kong. The inferred epidemic network displays significant effect on the propagation of infectious diseases.
Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage
Guo, Wenjuan; Cai, Yongli; Zhang, Qimin; Wang, Weiming
2018-02-01
This paper aims to study an SIS epidemic model with media coverage from a general deterministic model to a stochastic differential equation with environment fluctuation. Mathematically, we use the Markov semigroup theory to prove that the basic reproduction number R0s can be used to control the dynamics of stochastic system. Epidemiologically, we show that environment fluctuation can inhibit the occurrence of the disease, namely, in the case of disease persistence for the deterministic model, the disease still dies out with probability one for the stochastic model. So to a great extent the stochastic perturbation under media coverage affects the outbreak of the disease.
Epidemics in Networks : Modeling, Optimization and Security Games
Omic, J.
2010-01-01
Epidemic theory has wide range of applications in computer networks, from spreading of malware to the information dissemination algorithms. Our society depends more strongly than ever on such computer networks. Many of these networks rely to a large extent on decentralization and self-organization.
Siraj, A. S.; Oidtman, R. J.; Huber, J. H.; Kraemer, M. U.; Brady, O. J.; Johansson, M. A.; Perkins, T. A.
2017-12-01
Epidemic growth rate, r, provides a more complete description of the potential for epidemics than the more commonly studied basic reproduction number, R0, yet the former has never been described as a function of temperature for dengue virus or other pathogens with temperature-sensitive transmission. The need to understand the drivers of epidemics of these pathogens is acute, with arthropod-borne virus epidemics becoming increasingly problematic. We addressed this need by developing temperature-dependent descriptions of the two components of r—R0 and the generation interval—to obtain a temperature-dependent description of r. Our results show that the generation interval is highly sensitive to temperature, decreasing twofold between 25 and 35 °C and suggesting that dengue virus epidemics may accelerate as temperatures increase, not only because of more infections per generation but also because of faster generations. Under the empirical temperature relationships that we considered, we found that r peaked at a temperature threshold that was robust to uncertainty in model parameters that do not depend on temperature. Although the precise value of this temperature threshold could be refined following future studies of empirical temperature relationships, the framework we present for identifying such temperature thresholds offers a new way to classify regions in which dengue virus epidemic intensity could either increase or decrease under future climate change.
Bechah, Yassina; Capo, Christian; Mege, Jean-Louis; Raoult, Didier
2008-07-01
Epidemic typhus is transmitted to human beings by the body louse Pediculus humanus corporis. The disease is still considered a major threat by public-health authorities, despite the efficacy of antibiotics, because poor sanitary conditions are conducive to louse proliferation. Until recently, Rickettsia prowazekii, the causal agent, was thought to be confined to human beings and their body lice. Since 1975, R prowazekii infection in human beings has been related to contact with the flying squirrel Glaucomys volans in the USA. Moreover, Brill-Zinsser disease, a relapsed form of epidemic typhus that appears as sporadic cases many years after the initial infection, is unrelated to louse infestation. Stress or a waning immune system are likely to reactivate this earlier persistent infection, which could be the source of new epidemics when conditions facilitate louse infestation. Finally, R prowazekii is a potential category B bioterrorism agent, because it is stable in dried louse faeces and can be transmitted through aerosols. An increased understanding of the pathogenesis of epidemic typhus may be useful for protection against this bacterial threat.
Descriptive epidemiology of typhoid fever during an epidemic in Harare, Zimbabwe, 2012.
Polonsky, Jonathan A; Martínez-Pino, Isabel; Nackers, Fabienne; Chonzi, Prosper; Manangazira, Portia; Van Herp, Michel; Maes, Peter; Porten, Klaudia; Luquero, Francisco J
2014-01-01
Typhoid fever remains a significant public health problem in developing countries. In October 2011, a typhoid fever epidemic was declared in Harare, Zimbabwe - the fourth enteric infection epidemic since 2008. To orient control activities, we described the epidemiology and spatiotemporal clustering of the epidemic in Dzivaresekwa and Kuwadzana, the two most affected suburbs of Harare. A typhoid fever case-patient register was analysed to describe the epidemic. To explore clustering, we constructed a dataset comprising GPS coordinates of case-patient residences and randomly sampled residential locations (spatial controls). The scale and significance of clustering was explored with Ripley K functions. Cluster locations were determined by a random labelling technique and confirmed using Kulldorff's spatial scan statistic. We analysed data from 2570 confirmed and suspected case-patients, and found significant spatiotemporal clustering of typhoid fever in two non-overlapping areas, which appeared to be linked to environmental sources. Peak relative risk was more than six times greater than in areas lying outside the cluster ranges. Clusters were identified in similar geographical ranges by both random labelling and Kulldorff's spatial scan statistic. The spatial scale at which typhoid fever clustered was highly localised, with significant clustering at distances up to 4.5 km and peak levels at approximately 3.5 km. The epicentre of infection transmission shifted from one cluster to the other during the course of the epidemic. This study demonstrated highly localised clustering of typhoid fever during an epidemic in an urban African setting, and highlights the importance of spatiotemporal analysis for making timely decisions about targetting prevention and control activities and reinforcing treatment during epidemics. This approach should be integrated into existing surveillance systems to facilitate early detection of epidemics and identify their spatial range.
How to Estimate Epidemic Risk from Incomplete Contact Diaries Data?
Mastrandrea, Rossana; Barrat, Alain
2016-06-01
Social interactions shape the patterns of spreading processes in a population. Techniques such as diaries or proximity sensors allow to collect data about encounters and to build networks of contacts between individuals. The contact networks obtained from these different techniques are however quantitatively different. Here, we first show how these discrepancies affect the prediction of the epidemic risk when these data are fed to numerical models of epidemic spread: low participation rate, under-reporting of contacts and overestimation of contact durations in contact diaries with respect to sensor data determine indeed important differences in the outcomes of the corresponding simulations with for instance an enhanced sensitivity to initial conditions. Most importantly, we investigate if and how information gathered from contact diaries can be used in such simulations in order to yield an accurate description of the epidemic risk, assuming that data from sensors represent the ground truth. The contact networks built from contact sensors and diaries present indeed several structural similarities: this suggests the possibility to construct, using only the contact diary network information, a surrogate contact network such that simulations using this surrogate network give the same estimation of the epidemic risk as simulations using the contact sensor network. We present and compare several methods to build such surrogate data, and show that it is indeed possible to obtain a good agreement between the outcomes of simulations using surrogate and sensor data, as long as the contact diary information is complemented by publicly available data describing the heterogeneity of the durations of human contacts.
A network-based meta-population approach to model Rift Valley fever epidemics.
Xue, Ling; Scott, H Morgan; Cohnstaedt, Lee W; Scoglio, Caterina
2012-08-07
Rift Valley fever virus (RVFV) has been expanding its geographical distribution with important implications for both human and animal health. The emergence of Rift Valley fever (RVF) in the Middle East, and its continuing presence in many areas of Africa, has negatively impacted both medical and veterinary infrastructures and human morbidity, mortality, and economic endpoints. Furthermore, worldwide attention should be directed towards the broader infection dynamics of RVFV, because suitable host, vector and environmental conditions for additional epidemics likely exist on other continents; including Asia, Europe and the Americas. We propose a new compartmentalized model of RVF and the related ordinary differential equations to assess disease spread in both time and space; with the latter driven as a function of contact networks. Humans and livestock hosts and two species of vector mosquitoes are included in the model. The model is based on weighted contact networks, where nodes of the networks represent geographical regions and the weights represent the level of contact between regional pairings for each set of species. The inclusion of human, animal, and vector movements among regions is new to RVF modeling. The movement of the infected individuals is not only treated as a possibility, but also an actuality that can be incorporated into the model. We have tested, calibrated, and evaluated the model using data from the recent 2010 RVF outbreak in South Africa as a case study; mapping the epidemic spread within and among three South African provinces. An extensive set of simulation results shows the potential of the proposed approach for accurately modeling the RVF spreading process in additional regions of the world. The benefits of the proposed model are twofold: not only can the model differentiate the maximum number of infected individuals among different provinces, but also it can reproduce the different starting times of the outbreak in multiple locations
Estimating epidemic arrival times using linear spreading theory
Chen, Lawrence M.; Holzer, Matt; Shapiro, Anne
2018-01-01
We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is composed of a system of ordinary differential equations describing a meta-population susceptible-infected-recovered compartmental model defined on a network where each node represents a city and the edges represent the flight paths connecting cities. Making use of the linear determinacy of the system, we consider spreading speeds and arrival times in the system linearized about the unstable disease free state and compare these to arrival times in the nonlinear system. Two predictions are presented. The first is based upon expansion of the heat kernel for the linearized system. The second assumes that the dominant transmission pathway between any two cities can be approximated by a one dimensional lattice or a homogeneous tree and gives a uniform prediction for arrival times independent of the specific network features. We test these predictions on a real network describing worldwide airline traffic.
The influence of school holiday timing on epidemic impact.
Eames, K T D
2014-09-01
The impact of reactive school closure on an epidemic is uncertain, since it is not clear how an unplanned closure will affect social mixing patterns. The effect of school holidays on social mixing patterns is better understood. Here, we use mathematical models to explore the influence of the timing of school holidays on the final size and peak incidence of an influenza-like epidemic. A well-timed holiday can reduce the impact of an epidemic, in particular substantially reducing an epidemic's peak. Final size and peak incidence cannot both be minimized: a later holiday is optimal for minimizing the final size, while an earlier holiday minimizes peak incidence. Using social mixing data from the UK, we estimated that, had the 2009 influenza epidemic not been interrupted by the school summer holidays, the final size would have been about 20% larger and the peak about 170% higher.
Epidemic spread in bipartite network by considering risk awareness
Han, She; Sun, Mei; Ampimah, Benjamin Chris; Han, Dun
2018-02-01
Human awareness plays an important role in the spread of infectious diseases and the control of propagation patterns. Exploring the interplay between human awareness and epidemic spreading is a topic that has been receiving increasing attention. Considering the fact, some well-known diseases only spread between different species we propose a theoretical analysis of the Susceptible-Infected-Susceptible (SIS) epidemic spread from the perspective of bipartite network and risk aversion. Using mean field theory, the epidemic threshold is calculated theoretically. Simulation results are consistent with the proposed analytic model. The results show that, the final infection density is negative linear with the value of individuals' risk awareness. Therefore, the epidemic spread could be effectively suppressed by improving individuals' risk awareness.
Epidemic spreading on random surfer networks with infected avoidance strategy
International Nuclear Information System (INIS)
Feng Yun; Ding Li; Huang Yun-Han; Guan Zhi-Hong
2016-01-01
In this paper, we study epidemic spreading on random surfer networks with infected avoidance (IA) strategy. In particular, we consider that susceptible individuals’ moving direction angles are affected by the current location information received from infected individuals through a directed information network. The model is mainly analyzed by discrete-time numerical simulations. The results indicate that the IA strategy can restrain epidemic spreading effectively. However, when long-distance jumps of individuals exist, the IA strategy’s effectiveness on restraining epidemic spreading is heavily reduced. Finally, it is found that the influence of the noises from information transferring process on epidemic spreading is indistinctive. (paper)
Gönci, Balázs; Németh, Valéria; Balogh, Emeric; Szabó, Bálint; Dénes, Ádám; Környei, Zsuzsanna; Vicsek, Tamás
2010-12-20
Because of its relevance to everyday life, the spreading of viral infections has been of central interest in a variety of scientific communities involved in fighting, preventing and theoretically interpreting epidemic processes. Recent large scale observations have resulted in major discoveries concerning the overall features of the spreading process in systems with highly mobile susceptible units, but virtually no data are available about observations of infection spreading for a very large number of immobile units. Here we present the first detailed quantitative documentation of percolation-type viral epidemics in a highly reproducible in vitro system consisting of tens of thousands of virtually motionless cells. We use a confluent astroglial monolayer in a Petri dish and induce productive infection in a limited number of cells with a genetically modified herpesvirus strain. This approach allows extreme high resolution tracking of the spatio-temporal development of the epidemic. We show that a simple model is capable of reproducing the basic features of our observations, i.e., the observed behaviour is likely to be applicable to many different kinds of systems. Statistical physics inspired approaches to our data, such as fractal dimension of the infected clusters as well as their size distribution, seem to fit into a percolation theory based interpretation. We suggest that our observations may be used to model epidemics in more complex systems, which are difficult to study in isolation.
Beyond network structure: How heterogeneous susceptibility modulates the spread of epidemics.
Smilkov, Daniel; Hidalgo, Cesar A; Kocarev, Ljupco
2014-04-25
The compartmental models used to study epidemic spreading often assume the same susceptibility for all individuals, and are therefore, agnostic about the effects that differences in susceptibility can have on epidemic spreading. Here we show that-for the SIS model-differential susceptibility can make networks more vulnerable to the spread of diseases when the correlation between a node's degree and susceptibility are positive, and less vulnerable when this correlation is negative. Moreover, we show that networks become more likely to contain a pocket of infection when individuals are more likely to connect with others that have similar susceptibility (the network is segregated). These results show that the failure to include differential susceptibility to epidemic models can lead to a systematic over/under estimation of fundamental epidemic parameters when the structure of the networks is not independent from the susceptibility of the nodes or when there are correlations between the susceptibility of connected individuals.
Hattaf, Khalid; Mahrouf, Marouane; Adnani, Jihad; Yousfi, Noura
2018-01-01
In this paper, we propose a stochastic delayed epidemic model with specific functional response. The time delay represents temporary immunity period, i.e., time from recovery to becoming susceptible again. We first show that the proposed model is mathematically and biologically well-posed. Moreover, the extinction of the disease and the persistence in the mean are established in the terms of a threshold value R0S which is smaller than the basic reproduction number R0 of the corresponding deterministic system.
Chaos induced by breakup of waves in a spatial epidemic model with nonlinear incidence rate
International Nuclear Information System (INIS)
Sun, Gui-Quan; Jin, Zhen; Liu, Quan-Xing; Li, Li
2008-01-01
Spatial epidemiology is the study of spatial variation in disease risk or incidence, including the spatial patterns of the population. The spread of diseases in human populations can exhibit large scale patterns, underlining the need for spatially explicit approaches. In this paper, the spatiotemporal complexity of a spatial epidemic model with nonlinear incidence rate, which includes the behavioral changes and crowding effect of the infective individuals, is investigated. Based on both theoretical analysis and computer simulations, we find out when, under the parameters which can guarantee a stable limit cycle in the non-spatial model, spiral and target waves can emerge. Moreover, two different kinds of breakup of waves are shown. Specifically, the breakup of spiral waves is from the core and the breakup of target waves is from the far-field, and both kinds of waves become irregular patterns at last. Our results reveal that the spatiotemporal chaos is induced by the breakup of waves. The results obtained confirm that diffusion can form spiral waves, target waves or spatial chaos of high population density, which enrich the findings of spatiotemporal dynamics in the epidemic model
Epidemic spreading between two coupled subpopulations with inner structures
Ruan, Zhongyuan; Tang, Ming; Gu, Changgui; Xu, Jinshan
2017-10-01
The structure of underlying contact network and the mobility of agents are two decisive factors for epidemic spreading in reality. Here, we study a model consisting of two coupled subpopulations with intra-structures that emphasizes both the contact structure and the recurrent mobility pattern of individuals simultaneously. We show that the coupling of the two subpopulations (via interconnections between them and round trips of individuals) makes the epidemic threshold in each subnetwork to be the same. Moreover, we find that the interconnection probability between two subpopulations and the travel rate are important factors for spreading dynamics. In particular, as a function of interconnection probability, the epidemic threshold in each subpopulation decreases monotonously, which enhances the risks of an epidemic. While the epidemic threshold displays a non-monotonic variation as travel rate increases. Moreover, the asymptotic infected density as a function of travel rate in each subpopulation behaves differently depending on the interconnection probability.
Untangling the Interplay between Epidemic Spread and Transmission Network Dynamics.
Directory of Open Access Journals (Sweden)
Christel Kamp
Full Text Available The epidemic spread of infectious diseases is ubiquitous and often has a considerable impact on public health and economic wealth. The large variability in the spatio-temporal patterns of epidemics prohibits simple interventions and requires a detailed analysis of each epidemic with respect to its infectious agent and the corresponding routes of transmission. To facilitate this analysis, we introduce a mathematical framework which links epidemic patterns to the topology and dynamics of the underlying transmission network. The evolution, both in disease prevalence and transmission network topology, is derived from a closed set of partial differential equations for infections without allowing for recovery. The predictions are in excellent agreement with complementarily conducted agent-based simulations. The capacity of this new method is demonstrated in several case studies on HIV epidemics in synthetic populations: it allows us to monitor the evolution of contact behavior among healthy and infected individuals and the contributions of different disease stages to the spreading of the epidemic. This gives both direction to and a test bed for targeted intervention strategies for epidemic control. In conclusion, this mathematical framework provides a capable toolbox for the analysis of epidemics from first principles. This allows for fast, in silico modeling--and manipulation--of epidemics and is especially powerful if complemented with adequate empirical data for parameterization.
Directory of Open Access Journals (Sweden)
Wan Yang
2014-04-01
Full Text Available A variety of filtering methods enable the recursive estimation of system state variables and inference of model parameters. These methods have found application in a range of disciplines and settings, including engineering design and forecasting, and, over the last two decades, have been applied to infectious disease epidemiology. For any system of interest, the ideal filter depends on the nonlinearity and complexity of the model to which it is applied, the quality and abundance of observations being entrained, and the ultimate application (e.g. forecast, parameter estimation, etc.. Here, we compare the performance of six state-of-the-art filter methods when used to model and forecast influenza activity. Three particle filters--a basic particle filter (PF with resampling and regularization, maximum likelihood estimation via iterated filtering (MIF, and particle Markov chain Monte Carlo (pMCMC--and three ensemble filters--the ensemble Kalman filter (EnKF, the ensemble adjustment Kalman filter (EAKF, and the rank histogram filter (RHF--were used in conjunction with a humidity-forced susceptible-infectious-recovered-susceptible (SIRS model and weekly estimates of influenza incidence. The modeling frameworks, first validated with synthetic influenza epidemic data, were then applied to fit and retrospectively forecast the historical incidence time series of seven influenza epidemics during 2003-2012, for 115 cities in the United States. Results suggest that when using the SIRS model the ensemble filters and the basic PF are more capable of faithfully recreating historical influenza incidence time series, while the MIF and pMCMC do not perform as well for multimodal outbreaks. For forecast of the week with the highest influenza activity, the accuracies of the six model-filter frameworks are comparable; the three particle filters perform slightly better predicting peaks 1-5 weeks in the future; the ensemble filters are more accurate predicting peaks in
Dynamics of cholera epidemics with impulsive vaccination and disinfection.
Sisodiya, Omprakash Singh; Misra, O P; Dhar, Joydip
2018-04-01
Waterborne diseases have a tremendous influence on human life. The contaminated drinking water causes water-borne disease like cholera. Pulse vaccination is an important and effective strategy for the elimination of infectious diseases. A waterborne disease like cholera can also be controlled by using impulse technique. In this paper, we have proposed a delayed SEIRB epidemic model with impulsive vaccination and disinfection. We have studied the pulse vaccination strategy and sanitation to control the cholera disease. The existence and stability of the disease-free and endemic periodic solution are investigated both analytically and numerically. It is shown that there exists an infection-free periodic solution, using the impulsive dynamical system defined by the stroboscopic map. It is observed that the infection-free periodic solution is globally attractive when the impulse period is less than some critical value. From the analysis of the model, we have obtained a sufficient condition for the permanence of the epidemic with pulse vaccination. The main highlight of this paper is to introduce impulse technique along with latent period into the SEIRB epidemic model to investigate the role of pulse vaccination and disinfection on the dynamics of the cholera epidemics. Copyright © 2018 Elsevier Inc. All rights reserved.
Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence
International Nuclear Information System (INIS)
Zhang Tailei; Teng Zhidong
2008-01-01
In this paper, the asymptotic behavior of solutions of an autonomous SEIRS epidemic model with the saturation incidence is studied. Using the method of Liapunov-LaSalle invariance principle, we obtain the disease-free equilibrium is globally stable if the basic reproduction number is not greater than one. Moreover, we show that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions of locally and globally asymptotically stable convergence to an endemic equilibrium are obtained base on the permanence
Vaccination intervention on epidemic dynamics in networks
Peng, Xiao-Long; Xu, Xin-Jian; Fu, Xinchu; Zhou, Tao
2013-02-01
Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barabási-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations.
Spread of epidemic disease on networks
Newman, M. E.
2002-07-01
The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are nonuniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.
PROBLEM OF OPTIMAL CONTROL OF EPIDEMIC IN VIEW OF LATENT PERIOD
Directory of Open Access Journals (Sweden)
2017-01-01
Full Text Available The problem of optimal control of epidemic through vaccination and isolation, taking into account latent period is considered. The target function is minimized - functionality summarizing costs on epidemic prevention and treatment and also considering expenses on infected people left at the end of control T who may be a new source of epidemic. On the left endpoint of the integration segment initial data is given - quantity of infected and confirmed people at the moment t, the right endpoint is free. The dynamic constraints are written by way of a system of simple differential equations describing the speed of changes of number of subjected to infection and number of already infected. Besides the inhomogeneous communi- ty is considered, consisting of four age groups (babies, preschool children, school children and adults. The speed of vaccina- tion (number of vaccinated per a time unit and isolation speed are used as the control functions. There are some restrictions on control above and below. The latent period is described by the constant h and is part of the equation describing the con- tamination speed of people as a retarding in argument t, i.e. a person being in a latent period infects others not being aware of his disease. For problem solving Pontryagin maximum principle is used where it can be seen that the control is piecewise constant. The result of numerical implementation of discrete problem of optimal control is given. The conclusions are made that the latent period significantly influence the incidence rate and as consequence the costs on epidemic suppression. The programme based on the programming language Delphi gives an opportunity to estimate the scale of epidemic at different initial data and restrictions on control as well as to find an optimal control minimizing costs on epimedic suppression.
The impact of awareness on epidemic spreading in networks.
Wu, Qingchu; Fu, Xinchu; Small, Michael; Xu, Xin-Jian
2012-03-01
We explore the impact of awareness on epidemic spreading through a population represented by a scale-free network. Using a network mean-field approach, a mathematical model for epidemic spreading with awareness reactions is proposed and analyzed. We focus on the role of three forms of awareness including local, global, and contact awareness. By theoretical analysis and simulation, we show that the global awareness cannot decrease the likelihood of an epidemic outbreak while both the local awareness and the contact awareness can. Also, the influence degree of the local awareness on disease dynamics is closely related with the contact awareness.
Some models for epidemics of vector-transmitted diseases
Directory of Open Access Journals (Sweden)
Fred Brauer
2016-10-01
Full Text Available Vector-transmitted diseases such as dengue fever and chikungunya have been spreading rapidly in many parts of the world. The Zika virus has been known since 1947 and invaded South America in 2013. It can be transmitted not only by (mosquito vectors but also directly through sexual contact. Zika has developed into a serious global health problem because, while most cases are asymptomatic or very light, babies born to Zika - infected mothers may develop microcephaly and other very serious birth defects.We formulate and analyze two epidemic models for vector-transmitted diseases, one appropriate for dengue and chikungunya fever outbreaks and one that includes direct transmission appropriate for Zika virus outbreaks. This is especially important because the Zika virus is the first example of a disease that can be spread both indirectly through a vector and directly (through sexual contact. In both cases, we obtain expressions for the basic reproduction number and show how to use the initial exponential growth rate to estimate the basic reproduction number. However, for the model that includes direct transmission some additional data would be needed to identify the fraction of cases transmitted directly. Data for the 2015 Zika virus outbreak in Barranquilla, Colombia has been used to fit parameters to the model developed here and to estimate the basic reproduction number.
International Nuclear Information System (INIS)
Song Yu-Rong; Jiang Guo-Ping; Gong Yong-Wang
2013-01-01
In the propagation of an epidemic in a population, individuals adaptively adjust their behavior to avoid the risk of an epidemic. Differently from existing studies where new links are established randomly, a local link is established preferentially in this paper. We propose a new preferentially reconnecting edge strategy depending on spatial distance (PR-SD). For the PR-SD strategy, the new link is established at random with probability p and in a shortest distance with the probability 1 − p. We establish the epidemic model on an adaptive network using Cellular Automata, and demonstrate the effectiveness of the proposed model by numerical simulations. The results show that the smaller the value of parameter p, the more difficult the epidemic spread is. The PR-SD strategy breaks long-range links and establishes as many short-range links as possible, which causes the network efficiency to decrease quickly and the propagation of the epidemic is restrained effectively. (general)
Effect of risk perception on epidemic spreading in temporal networks
Moinet, Antoine; Pastor-Satorras, Romualdo; Barrat, Alain
2018-01-01
Many progresses in the understanding of epidemic spreading models have been obtained thanks to numerous modeling efforts and analytical and numerical studies, considering host populations with very different structures and properties, including complex and temporal interaction networks. Moreover, a number of recent studies have started to go beyond the assumption of an absence of coupling between the spread of a disease and the structure of the contacts on which it unfolds. Models including awareness of the spread have been proposed, to mimic possible precautionary measures taken by individuals that decrease their risk of infection, but have mostly considered static networks. Here, we adapt such a framework to the more realistic case of temporal networks of interactions between individuals. We study the resulting model by analytical and numerical means on both simple models of temporal networks and empirical time-resolved contact data. Analytical results show that the epidemic threshold is not affected by the awareness but that the prevalence can be significantly decreased. Numerical studies on synthetic temporal networks highlight, however, the presence of very strong finite-size effects, resulting in a significant shift of the effective epidemic threshold in the presence of risk awareness. For empirical contact networks, the awareness mechanism leads as well to a shift in the effective threshold and to a strong reduction of the epidemic prevalence.
On pulse vaccine strategy in a periodic stochastic SIR epidemic model
International Nuclear Information System (INIS)
Wang, Fengyan; Wang, Xiaoyi; Zhang, Shuwen; Ding, Changming
2014-01-01
A periodic stochastic SIR epidemic model with pulse vaccination is studied. The system has global positive solutions and under some conditions it admits a unique positive periodic disease-free solution, which is globally exponentially stable in mean square. The mathematical expectation and variance of the positive periodic solution are obtained. Two threshold parameters R 1 and R 2 (R 1 >R 2 ) are identified; if R 1 <1, the susceptible will be persistent in the mean and the disease will go to extinction; if R 2 >1, the susceptible and the disease will be weakly persistent in the mean. We show that by repeatedly vaccinating the susceptible population in series of pulses, it is possible to eradicate the infective from the entire model population in the random environment
The global dynamics for a stochastic SIS epidemic model with isolation
Chen, Yiliang; Wen, Buyu; Teng, Zhidong
2018-02-01
In this paper, we investigate the dynamical behavior for a stochastic SIS epidemic model with isolation which is as an important strategy for the elimination of infectious diseases. It is assumed that the stochastic effects manifest themselves mainly as fluctuation in the transmission coefficient, the death rate and the proportional coefficient of the isolation of infective. It is shown that the extinction and persistence in the mean of the model are determined by a threshold value R0S . That is, if R0S 1, then the disease is stochastic persistent in the means with probability one. Furthermore, the existence of a unique stationary distribution is discussed, and the sufficient conditions are established by using the Lyapunov function method. Finally, some numerical examples are carried out to confirm the analytical results.
Resolving epidemic network failures through differentiated repair times
DEFF Research Database (Denmark)
Fagertun, Anna Manolova; Ruepp, Sarah Renée; Manzano, Marc
2015-01-01
In this study, the authors investigate epidemic failure spreading in large-scale transport networks under generalisedmulti-protocol label switching control plane. By evaluating the effect of the epidemic failure spreading on the network,they design several strategies for cost-effective network pe...... assigninglower repair times among the network nodes. They believe that the event-driven simulation model can be highly beneficialfor network providers, since it could be used during the network planning process for facilitating cost-effective networksurvivability design.......In this study, the authors investigate epidemic failure spreading in large-scale transport networks under generalisedmulti-protocol label switching control plane. By evaluating the effect of the epidemic failure spreading on the network,they design several strategies for cost-effective network...... performance improvement via differentiated repair times. First, theyidentify the most vulnerable and the most strategic nodes in the network. Then, via extensive event-driven simulations theyshow that strategic placement of resources for improved failure recovery has better performance than randomly...
Directory of Open Access Journals (Sweden)
S Napp
Full Text Available Andalusia (Southern Spain is considered one of the main routes of introduction of bluetongue virus (BTV into Europe, evidenced by a devastating epidemic caused by BTV-1 in 2007. Understanding the pattern and the drivers of BTV-1 spread in Andalusia is critical for effective detection and control of future epidemics. A long-standing metric for quantifying the behaviour of infectious diseases is the case-reproduction ratio (Rt, defined as the average number of secondary cases arising from a single infected case at time t (for t>0. Here we apply a method using epidemic trees to estimate the between-herd case reproduction ratio directly from epidemic data allowing the spatial and temporal variability in transmission to be described. We then relate this variability to predictors describing the hosts, vectors and the environment to better understand why the epidemic spread more quickly in some regions or periods. The Rt value for the BTV-1 epidemic in Andalusia peaked in July at 4.6, at the start of the epidemic, then decreased to 2.2 by August, dropped below 1 by September (0.8, and by October it had decreased to 0.02. BTV spread was the consequence of both local transmission within established disease foci and BTV expansion to distant new areas (i.e. new foci, which resulted in a high variability in BTV transmission, not only among different areas, but particularly through time, which suggests that general control measures applied at broad spatial scales are unlikely to be effective. This high variability through time was probably due to the impact of temperature on BTV transmission, as evidenced by a reduction in the value of Rt by 0.0041 for every unit increase (day in the extrinsic incubation period (EIP, which is itself directly dependent on temperature. Moreover, within the range of values at which BTV-1 transmission occurred in Andalusia (20.6°C to 29.5°C there was a positive correlation between temperature and Rt values, although the
Directory of Open Access Journals (Sweden)
Balázs Gönci
2010-12-01
Full Text Available Because of its relevance to everyday life, the spreading of viral infections has been of central interest in a variety of scientific communities involved in fighting, preventing and theoretically interpreting epidemic processes. Recent large scale observations have resulted in major discoveries concerning the overall features of the spreading process in systems with highly mobile susceptible units, but virtually no data are available about observations of infection spreading for a very large number of immobile units. Here we present the first detailed quantitative documentation of percolation-type viral epidemics in a highly reproducible in vitro system consisting of tens of thousands of virtually motionless cells. We use a confluent astroglial monolayer in a Petri dish and induce productive infection in a limited number of cells with a genetically modified herpesvirus strain. This approach allows extreme high resolution tracking of the spatio-temporal development of the epidemic. We show that a simple model is capable of reproducing the basic features of our observations, i.e., the observed behaviour is likely to be applicable to many different kinds of systems. Statistical physics inspired approaches to our data, such as fractal dimension of the infected clusters as well as their size distribution, seem to fit into a percolation theory based interpretation. We suggest that our observations may be used to model epidemics in more complex systems, which are difficult to study in isolation.
Two-stage effects of awareness cascade on epidemic spreading in multiplex networks
Guo, Quantong; Jiang, Xin; Lei, Yanjun; Li, Meng; Ma, Yifang; Zheng, Zhiming
2015-01-01
Human awareness plays an important role in the spread of infectious diseases and the control of propagation patterns. The dynamic process with human awareness is called awareness cascade, during which individuals exhibit herd-like behavior because they are making decisions based on the actions of other individuals [Borge-Holthoefer et al., J. Complex Networks 1, 3 (2013), 10.1093/comnet/cnt006]. In this paper, to investigate the epidemic spreading with awareness cascade, we propose a local awareness controlled contagion spreading model on multiplex networks. By theoretical analysis using a microscopic Markov chain approach and numerical simulations, we find the emergence of an abrupt transition of epidemic threshold βc with the local awareness ratio α approximating 0.5 , which induces two-stage effects on epidemic threshold and the final epidemic size. These findings indicate that the increase of α can accelerate the outbreak of epidemics. Furthermore, a simple 1D lattice model is investigated to illustrate the two-stage-like sharp transition at αc≈0.5 . The results can give us a better understanding of why some epidemics cannot break out in reality and also provide a potential access to suppressing and controlling the awareness cascading systems.
Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control
Gao, Shujing; Zhong, Deming; Zhang, Yan
2018-04-01
In this paper, we establish two new stochastic switched epidemic models with continuous and impulsive control. The stochastic perturbations are considered for the natural death rate in each equation of the models. Firstly, a stochastic switched SILI model with continuous control schemes is investigated. By using Lyapunov-Razumikhin method, the sufficient conditions for extinction in mean are established. Our result shows that the disease could be die out theoretically if threshold value R is less than one, regardless of whether the disease-free solutions of the corresponding subsystems are stable or unstable. Then, a stochastic switched SILI model with continuous control schemes and pulse vaccination is studied. The threshold value R is derived. The global attractivity of the model is also obtained. At last, numerical simulations are carried out to support our results.
Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models.
Franke, John E; Yakubu, Abdul-Aziz
2008-12-01
The dynamics of simple discrete-time epidemic models without disease-induced mortality are typically characterized by global transcritical bifurcation. We prove that in corresponding models with disease-induced mortality a tiny number of infectious individuals can drive an otherwise persistent population to extinction. Our model with disease-induced mortality supports multiple attractors. In addition, we use a Ricker recruitment function in an SIS model and obtained a three component discrete Hopf (Neimark-Sacker) cycle attractor coexisting with a fixed point attractor. The basin boundaries of the coexisting attractors are fractal in nature, and the example exhibits sensitive dependence of the long-term disease dynamics on initial conditions. Furthermore, we show that in contrast to corresponding models without disease-induced mortality, the disease-free state dynamics do not drive the disease dynamics.
Leveraging social networks for understanding the evolution of epidemics
2011-01-01
Background To understand how infectious agents disseminate throughout a population it is essential to capture the social model in a realistic manner. This paper presents a novel approach to modeling the propagation of the influenza virus throughout a realistic interconnection network based on actual individual interactions which we extract from online social networks. The advantage is that these networks can be extracted from existing sources which faithfully record interactions between people in their natural environment. We additionally allow modeling the characteristics of each individual as well as customizing his daily interaction patterns by making them time-dependent. Our purpose is to understand how the infection spreads depending on the structure of the contact network and the individuals who introduce the infection in the population. This would help public health authorities to respond more efficiently to epidemics. Results We implement a scalable, fully distributed simulator and validate the epidemic model by comparing the simulation results against the data in the 2004-2005 New York State Department of Health Report (NYSDOH), with similar temporal distribution results for the number of infected individuals. We analyze the impact of different types of connection models on the virus propagation. Lastly, we analyze and compare the effects of adopting several different vaccination policies, some of them based on individual characteristics -such as age- while others targeting the super-connectors in the social model. Conclusions This paper presents an approach to modeling the propagation of the influenza virus via a realistic social model based on actual individual interactions extracted from online social networks. We implemented a scalable, fully distributed simulator and we analyzed both the dissemination of the infection and the effect of different vaccination policies on the progress of the epidemics. The epidemic values predicted by our simulator match
Leveraging social networks for understanding the evolution of epidemics
Directory of Open Access Journals (Sweden)
Martín Gonzalo
2011-12-01
Full Text Available Abstract Background To understand how infectious agents disseminate throughout a population it is essential to capture the social model in a realistic manner. This paper presents a novel approach to modeling the propagation of the influenza virus throughout a realistic interconnection network based on actual individual interactions which we extract from online social networks. The advantage is that these networks can be extracted from existing sources which faithfully record interactions between people in their natural environment. We additionally allow modeling the characteristics of each individual as well as customizing his daily interaction patterns by making them time-dependent. Our purpose is to understand how the infection spreads depending on the structure of the contact network and the individuals who introduce the infection in the population. This would help public health authorities to respond more efficiently to epidemics. Results We implement a scalable, fully distributed simulator and validate the epidemic model by comparing the simulation results against the data in the 2004-2005 New York State Department of Health Report (NYSDOH, with similar temporal distribution results for the number of infected individuals. We analyze the impact of different types of connection models on the virus propagation. Lastly, we analyze and compare the effects of adopting several different vaccination policies, some of them based on individual characteristics -such as age- while others targeting the super-connectors in the social model. Conclusions This paper presents an approach to modeling the propagation of the influenza virus via a realistic social model based on actual individual interactions extracted from online social networks. We implemented a scalable, fully distributed simulator and we analyzed both the dissemination of the infection and the effect of different vaccination policies on the progress of the epidemics. The epidemic values
Halasa, Tariq; Bøtner, Anette; Mortensen, Sten; Christensen, Hanne; Wulff, Sisse Birk; Boklund, Anette
2018-01-01
African swine fever (ASF) is a notifiable infectious disease. The disease is endemic in certain regions in Eastern Europe constituting a risk of ASF spread toward Western Europe. Therefore, as part of contingency planning, it is important to continuously explore strategies that can effectively control an epidemic of ASF. A previously published and well documented simulation model for ASF virus spread between herds was used to examine the epidemiologic and economic impacts of the duration and size of the control zones around affected herds. In the current study, scenarios were run, where the duration of the protection and surveillance zones were reduced from 50 and 45 days to 35 and 25 days or to 35 and 25 days, respectively. These scenarios were run with or without enlargement of the surveillance zone around detected herds from 10 to 15 km. The scenarios were also run with only clinical or clinical and serological surveillance of herds within the zones. Sensitivity analysis was conducted on influential input parameters in the model. The model predicts that reducing the duration of the protection and surveillance zones has no impact on the epidemiological consequences of the epidemics, while it may result in a substantial reduction in the total economic losses. In addition, the model predicts that increasing the size of the surveillance zone from 10 to 15 km may reduce both the epidemic duration and the total economic losses, in case of large epidemics. The ranking of the control strategies by the total costs of the epidemics was not influenced by changes of input parameters in the sensitivity analyses. PMID:29616228
Worm epidemics in wireless ad hoc networks
Energy Technology Data Exchange (ETDEWEB)
Nekovee, Maziar [BT Research, Polaris 134, Adastral Park, Martlesham, Suffolk IP5 3RE (United Kingdom); Centre for Computational Science, University College London, 20 Gordon Street, London WC1H 0AJ (United Kingdom)
2007-06-15
A dramatic increase in the number of computing devices with wireless communication capability has resulted in the emergence of a new class of computer worms which specifically target such devices. The most striking feature of these worms is that they do not require Internet connectivity for their propagation but can spread directly from device to device using a short-range radio communication technology, such as WiFi or Bluetooth. In this paper, we develop a new model for epidemic spreading of these worms and investigate their spreading in wireless ad hoc networks via extensive Monte Carlo simulations. Our studies show that the threshold behaviour and dynamics of worm epidemics in these networks are greatly affected by a combination of spatial and temporal correlations which characterize these networks, and are significantly different from the previously studied epidemics in the Internet.
Worm epidemics in wireless ad hoc networks
Nekovee, Maziar
2007-06-01
A dramatic increase in the number of computing devices with wireless communication capability has resulted in the emergence of a new class of computer worms which specifically target such devices. The most striking feature of these worms is that they do not require Internet connectivity for their propagation but can spread directly from device to device using a short-range radio communication technology, such as WiFi or Bluetooth. In this paper, we develop a new model for epidemic spreading of these worms and investigate their spreading in wireless ad hoc networks via extensive Monte Carlo simulations. Our studies show that the threshold behaviour and dynamics of worm epidemics in these networks are greatly affected by a combination of spatial and temporal correlations which characterize these networks, and are significantly different from the previously studied epidemics in the Internet.
Worm epidemics in wireless ad hoc networks
International Nuclear Information System (INIS)
Nekovee, Maziar
2007-01-01
A dramatic increase in the number of computing devices with wireless communication capability has resulted in the emergence of a new class of computer worms which specifically target such devices. The most striking feature of these worms is that they do not require Internet connectivity for their propagation but can spread directly from device to device using a short-range radio communication technology, such as WiFi or Bluetooth. In this paper, we develop a new model for epidemic spreading of these worms and investigate their spreading in wireless ad hoc networks via extensive Monte Carlo simulations. Our studies show that the threshold behaviour and dynamics of worm epidemics in these networks are greatly affected by a combination of spatial and temporal correlations which characterize these networks, and are significantly different from the previously studied epidemics in the Internet
Analysis of a Heroin Epidemic Model with Saturated Treatment Function
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Isaac Mwangi Wangari
2017-01-01
Full Text Available A mathematical model is developed that examines how heroin addiction spreads in society. The model is formulated to take into account the treatment of heroin users by incorporating a realistic functional form that “saturates” representing the limited availability of treatment. Bifurcation analysis reveals that the model has an intrinsic backward bifurcation whenever the saturation parameter is larger than a fixed threshold. We are particularly interested in studying the model’s global stability. In the absence of backward bifurcations, Lyapunov functions can often be found and used to prove global stability. However, in the presence of backward bifurcations, such Lyapunov functions may not exist or may be difficult to construct. We make use of the geometric approach to global stability to derive a condition that ensures that the system is globally asymptotically stable. Numerical simulations are also presented to give a more complete representation of the model dynamics. Sensitivity analysis performed by Latin hypercube sampling (LHS suggests that the effective contact rate in the population, the relapse rate of heroin users undergoing treatment, and the extent of saturation of heroin users are mechanisms fuelling heroin epidemic proliferation.
Epidemic models for phase transitions: application to a physical gel
Bilge, A. H.; Pekcan, O.; Kara, S.; Ogrenci, A. S.
2017-09-01
Carrageenan gels are characterized by reversible sol-gel and gel-sol transitions under cooling and heating processes and these transitions are approximated by generalized logistic growth curves. We express the transitions of carrageenan-water system, as a representative of reversible physical gels, in terms of a modified Susceptible-Infected-Susceptible epidemic model, as opposed to the Susceptible-Infected-Removed model used to represent the (irreversible) chemical gel formation in the previous work. We locate the gel point Tc of sol-gel and gel-sol transitions and we find that, for the sol-gel transition (cooling), Tc > Tsg (transition temperature), i.e. Tc is earlier in time for all carrageenan contents and moves forward in time and gets closer to Tsg as the carrageenan content increases. For the gel-sol transition (heating), Tc is relatively closer to Tgs; it is greater than Tgs, i.e. later in time for low carrageenan contents and moves backward as carrageenan content increases.
Scaling of the propagation of epidemics in a system of mobile agents
Gonzalez, M. C.; Herrmann, H. J.
2004-01-01
For a two-dimensional system of agents modeled by molecular dynamics, we simulate epidemics spreading, which was recently studied on complex networks. Our resulting network model is time-evolving. We study the transitions to spreading as function of density, temperature and infection time. In addition, we analyze the epidemic threshold associated to a power-law distribution of infection times.
Retrospective Analysis of the 2014-2015 Ebola Epidemic in Liberia.
Atkins, Katherine E; Pandey, Abhishek; Wenzel, Natasha S; Skrip, Laura; Yamin, Dan; Nyenswah, Tolbert G; Fallah, Mosoka; Bawo, Luke; Medlock, Jan; Altice, Frederick L; Townsend, Jeffrey; Ndeffo-Mbah, Martial L; Galvani, Alison P
2016-04-01
The 2014-2015 Ebola epidemic has been the most protracted and devastating in the history of the disease. To prevent future outbreaks on this scale, it is imperative to understand the reasons that led to eventual disease control. Here, we evaluated the shifts of Ebola dynamics at national and local scales during the epidemic in Liberia. We used a transmission model calibrated to epidemiological data between June 9 and December 31, 2014, to estimate the extent of community and hospital transmission. We found that despite varied local epidemic patterns, community transmission was reduced by 40-80% in all the counties analyzed. Our model suggests that the tapering of the epidemic was achieved through reductions in community transmission, rather than accumulation of immune individuals through asymptomatic infection and unreported cases. Although the times at which this transmission reduction occurred in the majority of the Liberian counties started before any large expansion in hospital capacity and the distribution of home protection kits, it remains difficult to associate the presence of interventions with reductions in Ebola incidence. © The American Society of Tropical Medicine and Hygiene.
A universal long-term flu vaccine may not prevent severe epidemics
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Blower Sally
2010-04-01
Full Text Available Abstract Background Recently, the promise of a new universal long-term flu vaccine has become more tangible than ever before. Such a vaccine would protect against very many seasonal and pandemic flu strains for many years, making annual vaccination unnecessary. However, due to complacency behavior, it remains unclear whether the introduction of such vaccines would maintain high and stable levels of vaccination coverage year after year. Findings To predict the impact of universal long-term flu vaccines on influenza epidemics we developed a mathematical model that linked human cognition and memory with the transmission dynamics of influenza. Our modeling shows that universal vaccines that provide short-term protection are likely to result in small frequent epidemics, whereas universal vaccines that provide long-term protection are likely to result in severe infrequent epidemics. Conclusions Influenza vaccines that provide short-term protection maintain risk awareness regarding influenza in the population and result in stable vaccination coverage. Vaccines that provide long-term protection could lead to substantial drops in vaccination coverage and should therefore include an annual epidemic risk awareness programs in order to minimize the risk of severe epidemics.
Epidemic spreading in weighted scale-free networks with community structure
International Nuclear Information System (INIS)
Chu, Xiangwei; Guan, Jihong; Zhang, Zhongzhi; Zhou, Shuigeng
2009-01-01
Many empirical studies reveal that the weights and community structure are ubiquitous in various natural and artificial networks. In this paper, based on the SI disease model, we investigate the epidemic spreading in weighted scale-free networks with community structure. Two exponents, α and β, are introduced to weight the internal edges and external edges, respectively; and a tunable probability parameter q is also introduced to adjust the strength of community structure. We find the external weighting exponent β plays a much more important role in slackening the epidemic spreading and reducing the danger brought by the epidemic than the internal weighting exponent α. Moreover, a novel result we find is that the strong community structure is no longer helpful for slackening the danger brought by the epidemic in the weighted cases. In addition, we show the hierarchical dynamics of the epidemic spreading in the weighted scale-free networks with communities which is also displayed in the famous BA scale-free networks
Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses
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Chuandong Li
2014-01-01
Full Text Available We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.
Sudden transitions in coupled opinion and epidemic dynamics with vaccination
Pires, Marcelo A.; Oestereich, André L.; Crokidakis, Nuno
2018-05-01
This work consists of an epidemic model with vaccination coupled with an opinion dynamics. Our objective was to study how disease risk perception can influence opinions about vaccination and therefore the spreading of the disease. Differently from previous works we have considered continuous opinions. The epidemic spreading is governed by an SIS-like model with an extra vaccinated state. In our model individuals vaccinate with a probability proportional to their opinions. The opinions change due to peer influence in pairwise interactions. The epidemic feedback to the opinion dynamics acts as an external field increasing the vaccination probability. We performed Monte Carlo simulations in fully-connected populations. Interestingly we observed the emergence of a first-order phase transition, besides the usual active-absorbing phase transition presented in the SIS model. Our simulations also show that with a certain combination of parameters, an increment in the initial fraction of the population that is pro-vaccine has a twofold effect: it can lead to smaller epidemic outbreaks in the short term, but it also contributes to the survival of the chain of infections in the long term. Our results also suggest that it is possible that more effective vaccines can decrease the long-term vaccine coverage. This is a counterintuitive outcome, but it is in line with empirical observations that vaccines can become a victim of their own success.
Epidemic spreading in multiplex networks influenced by opinion exchanges on vaccination.
Alvarez-Zuzek, Lucila G; La Rocca, Cristian E; Iglesias, José R; Braunstein, Lidia A
2017-01-01
Through years, the use of vaccines has always been a controversial issue. People in a society may have different opinions about how beneficial the vaccines are and as a consequence some of those individuals decide to vaccinate or not themselves and their relatives. This attitude in face of vaccines has clear consequences in the spread of diseases and their transformation in epidemics. Motivated by this scenario, we study, in a simultaneous way, the changes of opinions about vaccination together with the evolution of a disease. In our model we consider a multiplex network consisting of two layers. One of the layers corresponds to a social network where people share their opinions and influence others opinions. The social model that rules the dynamic is the M-model, which takes into account two different processes that occurs in a society: persuasion and compromise. This two processes are related through a parameter r, r 1 the society tends to have extremist opinions, while r = 1 represents a neutral society. This social network may be of real or virtual contacts. On the other hand, the second layer corresponds to a network of physical contacts where the disease spreading is described by the SIR-Model. In this model the individuals may be in one of the following four states: Susceptible (S), Infected(I), Recovered (R) or Vaccinated (V). A Susceptible individual can: i) get vaccinated, if his opinion in the other layer is totally in favor of the vaccine, ii) get infected, with probability β if he is in contact with an infected neighbor. Those I individuals recover after a certain period tr = 6. Vaccinated individuals have an extremist positive opinion that does not change. We consider that the vaccine has a certain effectiveness ω and as a consequence vaccinated nodes can be infected with probability β(1 - ω) if they are in contact with an infected neighbor. In this case, if the infection process is successful, the new infected individual changes his opinion from
Epidemic spreading in multiplex networks influenced by opinion exchanges on vaccination.
Directory of Open Access Journals (Sweden)
Lucila G Alvarez-Zuzek
Full Text Available Through years, the use of vaccines has always been a controversial issue. People in a society may have different opinions about how beneficial the vaccines are and as a consequence some of those individuals decide to vaccinate or not themselves and their relatives. This attitude in face of vaccines has clear consequences in the spread of diseases and their transformation in epidemics. Motivated by this scenario, we study, in a simultaneous way, the changes of opinions about vaccination together with the evolution of a disease. In our model we consider a multiplex network consisting of two layers. One of the layers corresponds to a social network where people share their opinions and influence others opinions. The social model that rules the dynamic is the M-model, which takes into account two different processes that occurs in a society: persuasion and compromise. This two processes are related through a parameter r, r 1 the society tends to have extremist opinions, while r = 1 represents a neutral society. This social network may be of real or virtual contacts. On the other hand, the second layer corresponds to a network of physical contacts where the disease spreading is described by the SIR-Model. In this model the individuals may be in one of the following four states: Susceptible (S, Infected(I, Recovered (R or Vaccinated (V. A Susceptible individual can: i get vaccinated, if his opinion in the other layer is totally in favor of the vaccine, ii get infected, with probability β if he is in contact with an infected neighbor. Those I individuals recover after a certain period tr = 6. Vaccinated individuals have an extremist positive opinion that does not change. We consider that the vaccine has a certain effectiveness ω and as a consequence vaccinated nodes can be infected with probability β(1 - ω if they are in contact with an infected neighbor. In this case, if the infection process is successful, the new infected individual changes his
HIV epidemics in Shenzhen and Chongqing, China.
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Shu Yang
Full Text Available Men who have sex with men (MSM and heterosexuals are the populations with the fastest growing HIV infection rates in China. We characterize the epidemic growth and age patterns between these two routes from 2004 to 2015 in Chongqing and Shenzhen, China.Data were downloaded from the National HIV/ AIDS Comprehensive Response Information Management System. For the new HIV diagnoses of heterosexuals and MSM in both cities, we estimated the growth rates by fitting different sub-exponential models. Heat maps are used to show their age patterns. We used histograms to compare these patterns by birth cohort.The MSM epidemics grew significantly in both cities. Chongqing experienced quadratic growth in HIV reported cases with an estimated growth rate of 0.086 per week and a "deceleration rate" of 0.673. HIV reported cases of MSM in Shenzhen grew even more drastically with a growth rate of 0.033 per week and "deceleration rate" of 0.794. The new infections are mainly affecting the ages of 18 to 30 in Chongqing and ages of 20 to 35 in Shenzhen. They peaked in early 1990's and mid-1990's birth cohorts in Chongqing and Shenzhen respectively. The HIV epidemic among heterosexuals grew rapidly in both cities. The growth rates were estimated as 0.02 and 0.028 in Chongqing and Shenzhen respectively whereas the "deceleration rates" were 0.878 and 0.790 in these two places. It affected mostly aged 18 to 75 in males and 18 to 65 in females in Chongqing and aged 18 to 45 in males and 18 to 50 in females in Shenzhen in 2015. In Chongqing, the heterosexual female epidemics display two peaks in HIV diagnoses in the birth cohorts of early 1950's and early 1980's, with heterosexual male epidemics peaked in early 1940's and early 1960's. The heterosexual male and female epidemics display higher rates in the birth cohort 1940-1960, than the birth cohort 1960-1990. It peaked in birth cohorts of 1950's and 1980's in Shenzhen.We revealed striking differences in epidemic growth
Multidimensional epidemic thresholds in diffusion processes over interdependent networks
International Nuclear Information System (INIS)
Salehi, Mostafa; Siyari, Payam; Magnani, Matteo; Montesi, Danilo
2015-01-01
Highlights: •We propose a new concept of multidimensional epidemic threshold for interdependent networks. •We analytically derive and numerically illustrate the conditions for multilayer epidemics. •We study the evolution of infection density and diffusion dynamics. -- Abstract: Several systems can be modeled as sets of interdependent networks where each network contains distinct nodes. Diffusion processes like the spreading of a disease or the propagation of information constitute fundamental phenomena occurring over such coupled networks. In this paper we propose a new concept of multidimensional epidemic threshold characterizing diffusion processes over interdependent networks, allowing different diffusion rates on the different networks and arbitrary degree distributions. We analytically derive and numerically illustrate the conditions for multilayer epidemics, i.e., the appearance of a giant connected component spanning all the networks. Furthermore, we study the evolution of infection density and diffusion dynamics with extensive simulation experiments on synthetic and real networks
Efficient control of epidemics spreading on networks: balance between treatment and recovery.
Oleś, Katarzyna; Gudowska-Nowak, Ewa; Kleczkowski, Adam
2013-01-01
We analyse two models describing disease transmission and control on regular and small-world networks. We use simulations to find a control strategy that minimizes the total cost of an outbreak, thus balancing the costs of disease against that of the preventive treatment. The models are similar in their epidemiological part, but differ in how the removed/recovered individuals are treated. The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease. However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results. Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models.
Hop limited epidemic-like information spreading in mobile social networks with selfish nodes
Wu, Yahui; Deng, Su; Huang, Hongbin
2013-07-01
Similar to epidemics, information can be transmitted directly among users in mobile social networks. Different from epidemics, we can control the spreading process by adjusting the corresponding parameters (e.g., hop count) directly. This paper proposes a theoretical model to evaluate the performance of an epidemic-like spreading algorithm, in which the maximal hop count of the information is limited. In addition, our model can be used to evaluate the impact of users’ selfish behavior. Simulations show the accuracy of our theoretical model. Numerical results show that the information hop count can have an important impact. In addition, the impact of selfish behavior is related to the information hop count.
Hop limited epidemic-like information spreading in mobile social networks with selfish nodes
International Nuclear Information System (INIS)
Wu, Yahui; Deng, Su; Huang, Hongbin
2013-01-01
Similar to epidemics, information can be transmitted directly among users in mobile social networks. Different from epidemics, we can control the spreading process by adjusting the corresponding parameters (e.g., hop count) directly. This paper proposes a theoretical model to evaluate the performance of an epidemic-like spreading algorithm, in which the maximal hop count of the information is limited. In addition, our model can be used to evaluate the impact of users’ selfish behavior. Simulations show the accuracy of our theoretical model. Numerical results show that the information hop count can have an important impact. In addition, the impact of selfish behavior is related to the information hop count. (paper)
Sequential detection of influenza epidemics by the Kolmogorov-Smirnov test
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Closas Pau
2012-10-01
Full Text Available Abstract Background Influenza is a well known and common human respiratory infection, causing significant morbidity and mortality every year. Despite Influenza variability, fast and reliable outbreak detection is required for health resource planning. Clinical health records, as published by the Diagnosticat database in Catalonia, host useful data for probabilistic detection of influenza outbreaks. Methods This paper proposes a statistical method to detect influenza epidemic activity. Non-epidemic incidence rates are modeled against the exponential distribution, and the maximum likelihood estimate for the decaying factor λ is calculated. The sequential detection algorithm updates the parameter as new data becomes available. Binary epidemic detection of weekly incidence rates is assessed by Kolmogorov-Smirnov test on the absolute difference between the empirical and the cumulative density function of the estimated exponential distribution with significance level 0 ≤ α ≤ 1. Results The main advantage with respect to other approaches is the adoption of a statistically meaningful test, which provides an indicator of epidemic activity with an associated probability. The detection algorithm was initiated with parameter λ0 = 3.8617 estimated from the training sequence (corresponding to non-epidemic incidence rates of the 2008-2009 influenza season and sequentially updated. Kolmogorov-Smirnov test detected the following weeks as epidemic for each influenza season: 50−10 (2008-2009 season, 38−50 (2009-2010 season, weeks 50−9 (2010-2011 season and weeks 3 to 12 for the current 2011-2012 season. Conclusions Real medical data was used to assess the validity of the approach, as well as to construct a realistic statistical model of weekly influenza incidence rates in non-epidemic periods. For the tested data, the results confirmed the ability of the algorithm to detect the start and the end of epidemic periods. In general, the proposed test could
GENERAL: Epidemic spreading on networks with vaccination
Shi, Hong-Jing; Duan, Zhi-Sheng; Chen, Guan-Rong; Li, Rong
2009-08-01
In this paper, a new susceptible-infected-susceptible (SIS) model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns (the recovered individuals have or have not immunity) on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine's effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.
Economic cost and burden of dengue during epidemics and non-epidemic years in Taiwan
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Dih-Ling Luh
2018-03-01
Full Text Available Background: Determining the disease and economic burden of dengue is critical for the allocation of public health resources. Several studies have used disability-adjusted life-years (DALYs to estimate the disease burden of dengue in different regions. However, there are no published studies discussing the estimates of dengue-related economic and disease burden specifically in Taiwan. Objectives: We assessed the economic cost and disease burden of dengue infections in Taiwan for the period 1998–2014, and compared these during epidemic and non-epidemic years. Methods: We estimated the annual DALYs per million population using the disability weights for dengue fever (DF, dengue hemorrhagic fever (DHF, dengue shock syndrome (DSS, and death cases. Economic costs were estimated and divided into direct (medical costs and indirect costs (lost work days and caregiver fees. Results: For the period 1998–2014, a mean of 115.3 (range: 6.3–934.3 DALYs per million population annually were lost to dengue. In epidemic years, direct costs associated with dengue resulted mostly from hospitalization (86.09%, emergency (7.77%, outpatient (6.10%, and drug costs (0.03%. For indirect costs, lost productivity due to death (70.76% was the dominant contributor. Overall, the costs were 12.3 times higher in epidemic years than in non-epidemic years (Wilcoxon rank sum test, p < 0.05. Conclusions: This study is the first to evaluate the economic costs and disease burden of dengue infections for this period in Taiwan, and reveals significant differences in economic impact between epidemic and non-epidemic years. Keywords: Economic cost of disease, Disease burden, Disability-adjusted life years (DALYs, Dengue, Epidemic
... Policy The Global HIV/AIDS Epidemic The Global HIV/AIDS Epidemic Published: Nov 29, 2017 Facebook Twitter ... 2001-FY 2018 Request The Global Response to HIV/AIDS International efforts to combat HIV began in ...
Sagar, Vikram; Zhao, Yi
2017-02-01
In the present work, the effect of personal behavior induced preventive measures is studied on the spread of epidemics over scale free networks that are characterized by the differential rate of disease transmission. The role of personal behavior induced preventive measures is parameterized in terms of variable λ, which modulates the number of concurrent contacts a node makes with the fraction of its neighboring nodes. The dynamics of the disease is described by a non-linear Susceptible Infected Susceptible model based upon the discrete time Markov Chain method. The network mean field approach is generalized to account for the effect of non-linear coupling between the aforementioned factors on the collective dynamics of nodes. The upper bound estimates of the disease outbreak threshold obtained from the mean field theory are found to be in good agreement with the corresponding non-linear stochastic model. From the results of parametric study, it is shown that the epidemic size has inverse dependence on the preventive measures (λ). It has also been shown that the increase in the average degree of the nodes lowers the time of spread and enhances the size of epidemics.
Recurrent epidemic cycles driven by intervention in a population of two susceptibility types
International Nuclear Information System (INIS)
Juanico, Drandreb Earl O
2014-01-01
Epidemics have been known to persist in the form of recurrence cycles. Despite intervention efforts through vaccination and targeted social distancing, infectious diseases like influenza continue to appear intermittently over time. I have undertaken an analysis of a stochastic epidemic model to explore the hypothesis that intervention efforts actually drive epidemic cycles. Time series from simulations of the model reveal oscillations exhibiting a similar temporal signature as influenza epidemics. The power-spectral density indicates a resonant frequency, which approximately corresponds to the apparent annual seasonality of influenza in temperate zones. Asymptotic solution to the backward Kolmogorov equation of the dynamics corresponds to an exponentially-decaying mean-exit time as a function of the intervention rate. Intervention must be implemented at a sufficiently high rate to extinguish the infection. The results demonstrate that intervention efforts can induce epidemic cycles, and that the temporal signature of cycles can provide early warning of imminent outbreaks
Long-range epidemic spreading in a random environment.
Juhász, Róbert; Kovács, István A; Iglói, Ferenc
2015-03-01
Modeling long-range epidemic spreading in a random environment, we consider a quenched, disordered, d-dimensional contact process with infection rates decaying with distance as 1/rd+σ. We study the dynamical behavior of the model at and below the epidemic threshold by a variant of the strong-disorder renormalization-group method and by Monte Carlo simulations in one and two spatial dimensions. Starting from a single infected site, the average survival probability is found to decay as P(t)∼t-d/z up to multiplicative logarithmic corrections. Below the epidemic threshold, a Griffiths phase emerges, where the dynamical exponent z varies continuously with the control parameter and tends to zc=d+σ as the threshold is approached. At the threshold, the spatial extension of the infected cluster (in surviving trials) is found to grow as R(t)∼t1/zc with a multiplicative logarithmic correction and the average number of infected sites in surviving trials is found to increase as Ns(t)∼(lnt)χ with χ=2 in one dimension.
Epidemic spreading and immunization strategy in multiplex networks
Alvarez Zuzek, Lucila G.; Buono, Camila; Braunstein, Lidia A.
2015-09-01
A more connected world has brought major consequences such as facilitate the spread of diseases all over the world to quickly become epidemics, reason why researchers are concentrated in modeling the propagation of epidemics and outbreaks in multilayer networks. In this networks all nodes interact in different layers with different type of links. However, in many scenarios such as in the society, a multiplex network framework is not completely suitable since not all individuals participate in all layers. In this paper, we use a partially overlapped, multiplex network where only a fraction of the individuals are shared by the layers. We develop a mitigation strategy for stopping a disease propagation, considering the Susceptible-Infected- Recover model, in a system consisted by two layers. We consider a random immunization in one of the layers and study the effect of the overlapping fraction in both, the propagation of the disease and the immunization strategy. Using branching theory, we study this scenario theoretically and via simulations and find a lower epidemic threshold than in the case without strategy.
Model checking biological systems described using ambient calculus
DEFF Research Database (Denmark)
Mardare, Radu Iulian; Priami, Corrado; Qualia, Paola
2005-01-01
Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005.......Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005....
Chimera states in multi-strain epidemic models with temporary immunity
Bauer, Larissa; Bassett, Jason; Hövel, Philipp; Kyrychko, Yuliya N.; Blyuss, Konstantin B.
2017-11-01
We investigate a time-delayed epidemic model for multi-strain diseases with temporary immunity. In the absence of cross-immunity between strains, dynamics of each individual strain exhibit emergence and annihilation of limit cycles due to a Hopf bifurcation of the endemic equilibrium, and a saddle-node bifurcation of limit cycles depending on the time delay associated with duration of temporary immunity. Effects of all-to-all and non-local coupling topologies are systematically investigated by means of numerical simulations, and they suggest that cross-immunity is able to induce a diverse range of complex dynamical behaviors and synchronization patterns, including discrete traveling waves, solitary states, and amplitude chimeras. Interestingly, chimera states are observed for narrower cross-immunity kernels, which can have profound implications for understanding the dynamics of multi-strain diseases.
Epidemic spreading on adaptively weighted scale-free networks.
Sun, Mengfeng; Zhang, Haifeng; Kang, Huiyan; Zhu, Guanghu; Fu, Xinchu
2017-04-01
We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation. We further analyze the effects of local information of diseases and various immunization schemes on epidemic dynamics. We also perform some stochastic network simulations which yield quantitative agreement with the deterministic mean-field approach.
Wang, Chenggang; Jiang, Baofa; Fan, Jingchun; Wang, Furong; Liu, Qiyong
2014-01-01
The aim of this study is to develop a model that correctly identifies and quantifies the relationship between dengue and meteorological factors in Guangzhou, China. By cross-correlation analysis, meteorological variables and their lag effects were determined. According to the epidemic characteristics of dengue in Guangzhou, those statistically significant variables were modeled by a zero-inflated Poisson regression model. The number of dengue cases and minimum temperature at 1-month lag, along with average relative humidity at 0- to 1-month lag were all positively correlated with the prevalence of dengue fever, whereas wind velocity and temperature in the same month along with rainfall at 2 months' lag showed negative association with dengue incidence. Minimum temperature at 1-month lag and wind velocity in the same month had a greater impact on the dengue epidemic than other variables in Guangzhou.
Hepatitis E epidemics in India
Indian Academy of Sciences (India)
The first well recorded epidemic was in 1955-56 here in Delhi with nearly 30000 cases. Large outbreaks occurred in 1978 in Kashmir. My interest in this disease began in 1991 during investigations into a large epidemic of hepatitis E in Kanpur that my mentor, later Prof SR Naik, and I undertook. I will use this epidemic as an ...
Epidemic spreading on random surfer networks with infected avoidance strategy
Feng, Yun; Ding, Li; Huang, Yun-Han; Guan, Zhi-Hong
2016-12-01
In this paper, we study epidemic spreading on random surfer networks with infected avoidance (IA) strategy. In particular, we consider that susceptible individuals’ moving direction angles are affected by the current location information received from infected individuals through a directed information network. The model is mainly analyzed by discrete-time numerical simulations. The results indicate that the IA strategy can restrain epidemic spreading effectively. However, when long-distance jumps of individuals exist, the IA strategy’s effectiveness on restraining epidemic spreading is heavily reduced. Finally, it is found that the influence of the noises from information transferring process on epidemic spreading is indistinctive. Project supported in part by the National Natural Science Foundation of China (Grant Nos. 61403284, 61272114, 61673303, and 61672112) and the Marine Renewable Energy Special Fund Project of the State Oceanic Administration of China (Grant No. GHME2013JS01).
DEFF Research Database (Denmark)
Chowell, Gerardo; Hincapie-Palacio, Doracelly; Ospina, Juan
2016-01-01
BACKGROUND: The World Health Organization declared the ongoing Zika virus (ZIKV) epidemic in the Americas a Public Health Emergency of International Concern on February 1, 2016. ZIKV disease in humans is characterized by a "dengue-like" syndrome including febrile illness and rash. However, ZIKV...... impact. METHODS: We obtained daily counts of suspected Zika cases by date of symptoms onset from the Secretary of Health of Antioquia, Colombia during January-April 2016. We calibrated the generalized Richards model, a phenomenological model that accommodates a variety of early exponential and sub...
The importance of thinking beyond the water-supply in cholera epidemics
DEFF Research Database (Denmark)
Phelps, Matthew D.; Azman, Andrew S.; Lewnard, Joseph A.
2017-01-01
the contribution of long-cycle waterborne transmission between neighborhoods using historical municipal water infrastructure data, fitting the force of infection from hydraulic flow, then comparing model performance. We found the epidemic was characterized by considerable transmission heterogeneity. Some...... municipal water quality. We recommend public health planners consider programs aimed at interrupting short-cycle transmission as essential tools in the cholera control arsenal. Author summary: John Snow’s seminal work on the London cholera epidemic and Broadway pump helped establish cholera......-cycle transmission to the epidemic. We find transmission between neighborhoods during the epidemic did not follow water pipe connections, suggesting little evidence of long-cycle transmission. Instead, we suggest that short-cycle transmission was likely critical to the propagation of the outbreak. Interventions...
Optimal control of epidemic information dissemination over networks.
Chen, Pin-Yu; Cheng, Shin-Ming; Chen, Kwang-Cheng
2014-12-01
Information dissemination control is of crucial importance to facilitate reliable and efficient data delivery, especially in networks consisting of time-varying links or heterogeneous links. Since the abstraction of information dissemination much resembles the spread of epidemics, epidemic models are utilized to characterize the collective dynamics of information dissemination over networks. From a systematic point of view, we aim to explore the optimal control policy for information dissemination given that the control capability is a function of its distribution time, which is a more realistic model in many applications. The main contributions of this paper are to provide an analytically tractable model for information dissemination over networks, to solve the optimal control signal distribution time for minimizing the accumulated network cost via dynamic programming, and to establish a parametric plug-in model for information dissemination control. In particular, we evaluate its performance in mobile and generalized social networks as typical examples.
Susceptible-infected-susceptible epidemics on networks with general infection and cure times
Cator, E.; van de Bovenkamp, R.; Van Mieghem, P.
2013-06-01
The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous N-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.
International Nuclear Information System (INIS)
El-Doma, M.
2001-02-01
The stability of the endemic equilibrium of an SIS age-structured epidemic model of a vertically as well as horizontally transmitted disease is investigated when the force of infection is of proportionate mixing assumption type. We also investigate the uniform weak disease persistence. (author)
The spatial resolution of epidemic peaks.
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Harriet L Mills
2014-04-01
Full Text Available The emergence of novel respiratory pathogens can challenge the capacity of key health care resources, such as intensive care units, that are constrained to serve only specific geographical populations. An ability to predict the magnitude and timing of peak incidence at the scale of a single large population would help to accurately assess the value of interventions designed to reduce that peak. However, current disease-dynamic theory does not provide a clear understanding of the relationship between: epidemic trajectories at the scale of interest (e.g. city; population mobility; and higher resolution spatial effects (e.g. transmission within small neighbourhoods. Here, we used a spatially-explicit stochastic meta-population model of arbitrary spatial resolution to determine the effect of resolution on model-derived epidemic trajectories. We simulated an influenza-like pathogen spreading across theoretical and actual population densities and varied our assumptions about mobility using Latin-Hypercube sampling. Even though, by design, cumulative attack rates were the same for all resolutions and mobilities, peak incidences were different. Clear thresholds existed for all tested populations, such that models with resolutions lower than the threshold substantially overestimated population-wide peak incidence. The effect of resolution was most important in populations which were of lower density and lower mobility. With the expectation of accurate spatial incidence datasets in the near future, our objective was to provide a framework for how to use these data correctly in a spatial meta-population model. Our results suggest that there is a fundamental spatial resolution for any pathogen-population pair. If underlying interactions between pathogens and spatially heterogeneous populations are represented at this resolution or higher, accurate predictions of peak incidence for city-scale epidemics are feasible.
Review. Systems for prevention and control of epidemic emergencies
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Paolo Calistri
2013-09-01
Full Text Available The development of early warning systems is fundamental for preventing the spread of infectious diseases. Data collection, however, is a costly activity and it is not possible to implement early warning systems everywhere and for all possible events. Hence, tools helping to improve the focus of surveillance efforts are of paramount importance. Risk assessment methods and other provisional modelling techniques may permit to estimate the probability of introduction and spread of infectious diseases in different geographical areas. Similarly, efficient information systems must be in place to assist the veterinary services in case of epidemic emergencies in order to support the prompt application of control measures for the containment of the infection and the reduction of the magnitude of negative consequences. This review describes two recent approaches to the estimation of the probability of introduction and spread of infectious diseases based on the use of risk maps/spatial modelling and Social Network Analysis (SNA techniques. The review also describes a web application developed in Italy to help official veterinary services to trace animals in case of outbreaks of infectious diseases.
Retrospective Analysis of the 2014–2015 Ebola Epidemic in Liberia
Atkins, Katherine E.; Pandey, Abhishek; Wenzel, Natasha S.; Skrip, Laura; Yamin, Dan; Nyenswah, Tolbert G.; Fallah, Mosoka; Bawo, Luke; Medlock, Jan; Altice, Frederick L.; Townsend, Jeffrey; Ndeffo-Mbah, Martial L.; Galvani, Alison P.
2016-01-01
The 2014–2015 Ebola epidemic has been the most protracted and devastating in the history of the disease. To prevent future outbreaks on this scale, it is imperative to understand the reasons that led to eventual disease control. Here, we evaluated the shifts of Ebola dynamics at national and local scales during the epidemic in Liberia. We used a transmission model calibrated to epidemiological data between June 9 and December 31, 2014, to estimate the extent of community and hospital transmission. We found that despite varied local epidemic patterns, community transmission was reduced by 40–80% in all the counties analyzed. Our model suggests that the tapering of the epidemic was achieved through reductions in community transmission, rather than accumulation of immune individuals through asymptomatic infection and unreported cases. Although the times at which this transmission reduction occurred in the majority of the Liberian counties started before any large expansion in hospital capacity and the distribution of home protection kits, it remains difficult to associate the presence of interventions with reductions in Ebola incidence. PMID:26928839
Efficient control of epidemics spreading on networks: balance between treatment and recovery.
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Katarzyna Oleś
Full Text Available We analyse two models describing disease transmission and control on regular and small-world networks. We use simulations to find a control strategy that minimizes the total cost of an outbreak, thus balancing the costs of disease against that of the preventive treatment. The models are similar in their epidemiological part, but differ in how the removed/recovered individuals are treated. The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease. However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment the models give similar results. Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models.
Information Spreading in Epidemics and in Communication Networks
DEFF Research Database (Denmark)
Uekermann, Florian Philipp
The PhD thesis revolves mainly around models of disease spreading and human behavior. We present models for different epidemic patterns of infectious diseases. This includes investigations of the trajectory of the 2014 Ebola outbreak in West-Africa, influenza evolution and the seasonal dynamics...
Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package surveillance
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Sebastian Meyer
2017-05-01
Full Text Available The availability of geocoded health data and the inherent temporal structure of communicable diseases have led to an increased interest in statistical models and software for spatio-temporal data with epidemic features. The open source R package surveillance can handle various levels of aggregation at which infective events have been recorded: individual-level time-stamped geo-referenced data (case reports in either continuous space or discrete space, as well as counts aggregated by period and region. For each of these data types, the surveillance package implements tools for visualization, likelihoood inference and simulation from recently developed statistical regression frameworks capturing endemic and epidemic dynamics. Altogether, this paper is a guide to the spatio-temporal modeling of epidemic phenomena, exemplified by analyses of public health surveillance data on measles and invasive meningococcal disease.
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Jiancang Zhuang
2012-07-01
Full Text Available Based on the ETAS (epidemic-type aftershock sequence model, which is used for describing the features of short-term clustering of earthquake occurrence, this paper presents some theories and techniques related to evaluating the probability distribution of the maximum magnitude in a given space-time window, where the Gutenberg-Richter law for earthquake magnitude distribution cannot be directly applied. It is seen that the distribution of the maximum magnitude in a given space-time volume is determined in the longterm by the background seismicity rate and the magnitude distribution of the largest events in each earthquake cluster. The techniques introduced were applied to the seismicity in the Japan region in the period from 1926 to 2009. It was found that the regions most likely to have big earthquakes are along the Tohoku (northeastern Japan Arc and the Kuril Arc, both with much higher probabilities than the offshore Nankai and Tokai regions.
Epidemic extinction paths in complex networks
Hindes, Jason; Schwartz, Ira B.
2017-05-01
We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic susceptible-infected-susceptible model, we predict the distribution of large fluctuations, the most probable or optimal path through a network that leads to a disease-free state from an endemic state, and the average extinction time in general configurations. Our predictions agree with Monte Carlo simulations on several networks, including synthetic weighted and degree-distributed networks with degree correlations, and an empirical high school contact network. In addition, our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations, both near and away from the epidemic threshold, in networks with heterogeneous eigenvector centrality and degree distributions.
Liu, Can; Xie, Jia-Rong; Chen, Han-Shuang; Zhang, Hai-Feng; Tang, Ming
2015-10-01
The spreading of an infectious disease can trigger human behavior responses to the disease, which in turn plays a crucial role on the spreading of epidemic. In this study, to illustrate the impacts of the human behavioral responses, a new class of individuals, S(F), is introduced to the classical susceptible-infected-recovered model. In the model, S(F) state represents that susceptible individuals who take self-initiate protective measures to lower the probability of being infected, and a susceptible individual may go to S(F) state with a response rate when contacting an infectious neighbor. Via the percolation method, the theoretical formulas for the epidemic threshold as well as the prevalence of epidemic are derived. Our finding indicates that, with the increasing of the response rate, the epidemic threshold is enhanced and the prevalence of epidemic is reduced. The analytical results are also verified by the numerical simulations. In addition, we demonstrate that, because the mean field method neglects the dynamic correlations, a wrong result based on the mean field method is obtained-the epidemic threshold is not related to the response rate, i.e., the additional S(F) state has no impact on the epidemic threshold.
Siettos, Constantinos; Anastassopoulou, Cleo; Russo, Lucia; Grigoras, Christos; Mylonakis, Eleftherios
2015-03-09
We developed an agent-based model to investigate the epidemic dynamics of Ebola virus disease (EVD) in Liberia and Sierra Leone from May 27 to December 21, 2014. The dynamics of the agent-based simulator evolve on small-world transmission networks of sizes equal to the population of each country, with adjustable densities to account for the effects of public health intervention policies and individual behavioral responses to the evolving epidemic. Based on time series of the official case counts from the World Health Organization (WHO), we provide estimates for key epidemiological variables by employing the so-called Equation-Free approach. The underlying transmission networks were characterized by rather random structures in the two countries with densities decreasing by ~19% from the early (May 27-early August) to the last period (mid October-December 21). Our estimates for the values of key epidemiological variables, such as the mean time to death, recovery and the case fatality rate, are very close to the ones reported by the WHO Ebola response team during the early period of the epidemic (until September 14) that were calculated based on clinical data. Specifically, regarding the effective reproductive number Re, our analysis suggests that until mid October, Re was above 2.3 in both countries; from mid October to December 21, Re dropped well below unity in Liberia, indicating a saturation of the epidemic, while in Sierra Leone it was around 1.9, indicating an ongoing epidemic. Accordingly, a ten-week projection from December 21 estimated that the epidemic will fade out in Liberia in early March; in contrast, our results flashed a note of caution for Sierra Leone since the cumulative number of cases could reach as high as 18,000, and the number of deaths might exceed 5,000, by early March 2015. However, by processing the reported data of the very last period (December 21, 2014-January 18, 2015), we obtained more optimistic estimates indicative of a remission of
Phase Transitions of an Epidemic Spreading Model in Small-World Networks
Hua, Da-Yin; Gao, Ke
2011-06-01
We propose a modified susceptible-infected-refractory-susceptible (SIRS) model to investigate the global oscillations of the epidemic spreading in Watts—Strogatz (WS) small-world networks. It is found that when an individual immunity does not change or decays slowly in an immune period, the system can exhibit complex transition from an infecting stationary state to a large amplitude sustained oscillation or an absorbing state with no infection. When the immunity decays rapidly in the immune period, the transition to the global oscillation disappears and there is no oscillation. Furthermore, based on the spatio-temporal evolution patterns and the phase diagram, it is disclosed that a long immunity period takes an important role in the emergence of the global oscillation in small-world networks.
Optimal solutions for the evolution of a social obesity epidemic model
Sikander, Waseem; Khan, Umar; Mohyud-Din, Syed Tauseef
2017-06-01
In this work, a novel modification in the traditional homotopy perturbation method (HPM) is proposed by embedding an auxiliary parameter in the boundary condition. The scheme is used to carry out a mathematical evaluation of the social obesity epidemic model. The incidence of excess weight and obesity in adulthood population and prediction of its behavior in the coming years is analyzed by using a modified algorithm. The proposed method increases the convergence of the approximate analytical solution over the domain of the problem. Furthermore, a convenient way is considered for choosing an optimal value of auxiliary parameters via minimizing the total residual error. The graphical comparison of the obtained results with the standard HPM explicitly reveals the accuracy and efficiency of the developed scheme.
Stochastic Processes in Epidemic Theory
Lefèvre, Claude; Picard, Philippe
1990-01-01
This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.
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Myriam Khlat
2016-12-01
Full Text Available The original four-stage model of the cigarette epidemic has been extended with diffusion of innovations theory to reflect socio-economic differences in cigarette use. Recently, two revisions of the model have been proposed: (1 separate analysis of the epidemic stages for men and women, in order to improve generalization to developing countries, and; (2 addition of a fifth stage to the smoking epidemic, in order to account for the persistence of smoking in disadvantaged social groups. By developing a cohort perspective spanning a 35-year time period in France and the USA, we uncover distinctive features which challenge the currently held vision on the evolution of smoking inequalities within the framework of the cigarette epidemic. We argue that the reason for which the model may not be fit to the lower educated is that the imitation mechanism underlying the diffusion of innovations works well with regard to adoption of the habit, but is much less relevant with regard to its rejection. Based on those observations, we support the idea that the nature and timing of the epidemic differs enough to treat the stages separately for high and low education groups, and discuss policy implications.
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Denton Miles
2008-06-01
Full Text Available Abstract Background Cystic fibrosis (CF is an inherited multi-system disorder characterised by chronic airway infection with pathogens such as Pseudomonas aeruginosa. Acquisition of P. aeruginosa by patients with CF is usually from the environment, but recent studies have demonstrated patient to patient transmission of certain epidemic strains, possibly via an airborne route. This study was designed to examine the survival of P. aeruginosa within artificially generated aerosols. Results Survival was effected by the solution used for aerosol generation. Within the aerosols it was adversely affected by an increase in air temperature. Both epidemic and non-epidemic strains of P. aeruginosa were able to survive within the aerosols, but strains expressing a mucoid phenotype had a survival advantage. Conclusion This would suggest that segregating individuals free of P. aeruginosa from those with chronic P. aeruginosa infection who are more likely to be infected with mucoid strains may help reduce the risk of cross-infection. Environmental factors also appear to influence bacterial survival. Warming and drying the air within clinical areas and avoidance of humidification devices may also be beneficial in reducing the risk of cross-infection.
Modeling sheep pox disease from the 1994-1998 epidemic in Evros Prefecture, Greece.
Malesios, C; Demiris, N; Abas, Z; Dadousis, K; Koutroumanidis, T
2014-10-01
Sheep pox is a highly transmissible disease which can cause serious loss of livestock and can therefore have major economic impact. We present data from sheep pox epidemics which occurred between 1994 and 1998. The data include weekly records of infected farms as well as a number of covariates. We implement Bayesian stochastic regression models which, in addition to various explanatory variables like seasonal and environmental/meteorological factors, also contain serial correlation structure based on variants of the Ornstein-Uhlenbeck process. We take a predictive view in model selection by utilizing deviance-based measures. The results indicate that seasonality and the number of infected farms are important predictors for sheep pox incidence. Copyright © 2014 Elsevier Ltd. All rights reserved.
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Jessica Duong
Full Text Available Epidemic strains of Pseudomonas aeruginosa have been found worldwide among the cystic fibrosis (CF patient population. Using pulse-field gel electrophoresis, the Prairie Epidemic Strain (PES has recently been found in one-third of patients attending the Calgary Adult CF Clinic in Canada. Using multi-locus sequence typing, PES isolates from unrelated patients were found to consistently have ST192. Though most patients acquired PES prior to enrolling in the clinic, some patients were observed to experience strain replacement upon transitioning to the clinic whereby local non-epidemic P. aeruginosa isolates were displaced by PES. Here we genotypically and phenotypically compared PES to other P. aeruginosa epidemic strains (OES found around the world as well as local non-epidemic CF P. aeruginosa isolates in order to characterize PES. Since some epidemic strains are associated with worse clinical outcomes, we assessed the pathogenic potential of PES to determine if these isolates are virulent, shared properties with OES, and if its phenotypic properties may offer a competitive advantage in displacing local non-epidemic isolates during strain replacement. As such, we conducted a comparative analysis using fourteen phenotypic traits, including virulence factor production, biofilm formation, planktonic growth, mucoidy, and antibiotic susceptibility to characterize PES, OES, and local non-epidemic isolates. We observed that PES and OES could be differentiated from local non-epidemic isolates based on biofilm growth with PES isolates being more mucoid. Pairwise comparisons indicated that PES produced significantly higher levels of proteases and formed better biofilms than OES but were more susceptible to antibiotic treatment. Amongst five patients experiencing strain replacement, we found that super-infecting PES produced lower levels of proteases and elastases but were more resistant to antibiotics compared to the displaced non-epidemic isolates. This
Reconstructing the AIDS epidemic among injection drug users in Brazil.
Hacker, Mariana A; Leite, Iuri C; Renton, Adrian; Torres, Tania Guillén de; Gracie, Renata; Bastos, Francisco I
2006-04-01
The HIV/AIDS epidemic among injection drug users (IDUs) in Brazil has been unique in terms of temporal and geographical contrasts. This analysis explores these contrasts through the use of multilevel modeling. Standardized AIDS incidence rates among IDUs for Brazilian municipalities (1986-2000) were used as the dependent variable, with a set of social indicators as independent variables (covariates). In some States of the North/Northeast, the epidemic among IDUs has been incipient. The São Paulo epidemic extended to reach a network of municipalities, most of which located far from the capital. More recently, on a smaller scale, a similar extension has been observed in the southernmost States of the country. Both "number of physicians per inhabitant" and "standard distance to the State capital" were found to be associated with AIDS incidence. AIDS cases among IDUs appeared to cluster in wealthier, more developed municipalities. The relative weight of such extensive dissemination in key, heavily populated States prevails in the Brazilian IDU epidemic, defining a central-western-southeastern strip of wealthier middle-sized municipalities and more recently a southern strip of municipalities deeply affected by the epidemic in this population.
Reconstructing the AIDS epidemic among injection drug users in Brazil
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Mariana A. Hacker
2006-04-01
Full Text Available The HIV/AIDS epidemic among injection drug users (IDUs in Brazil has been unique in terms of temporal and geographical contrasts. This analysis explores these contrasts through the use of multilevel modeling. Standardized AIDS incidence rates among IDUs for Brazilian municipalities (1986-2000 were used as the dependent variable, with a set of social indicators as independent variables (covariates. In some States of the North/Northeast, the epidemic among IDUs has been incipient. The São Paulo epidemic extended to reach a network of municipalities, most of which located far from the capital. More recently, on a smaller scale, a similar extension has been observed in the southernmost States of the country. Both "number of physicians per inhabitant" and "standard distance to the State capital" were found to be associated with AIDS incidence. AIDS cases among IDUs appeared to cluster in wealthier, more developed municipalities. The relative weight of such extensive dissemination in key, heavily populated States prevails in the Brazilian IDU epidemic, defining a central-western-southeastern strip of wealthier middle-sized municipalities and more recently a southern strip of municipalities deeply affected by the epidemic in this population.
Thacker, Stephen B; Stroup, Donna F; Sencer, David J
2011-12-01
Since 1946, the Centers for Disease Control and Prevention has responded to urgent requests from US states, federal agencies, and international organizations through epidemic-assistance investigations (Epi-Aids). The authors describe the first 60 years of Epi-Aids, breadth of problems addressed, evolution of methodologies, scope of activities, and impact of investigations on population health. They reviewed Epi-Aid reports and EIS Bulletins, contacted current and former Epidemic Intelligence Service staff, and systematically searched the PubMed and Web of Science databases. They abstracted information on dates, location, staff involved, health problems, methods, and impacts of investigations according to a preplanned protocol. They assessed the methods presented as well as the quality of reports. During 1946-2005, a total of 4,484 investigations of health events were initiated by 2,815 Epidemic Intelligence Service officers. In the early years, the majority were in response to infectious agents, although environmental problems emerged. Investigations in subsequent years focused on occupational conditions, birth defects, reproductive health, tobacco use, cancer, violence, legal debate, and terrorism. These Epi-Aids heralded expansion of the agency's mission and presented new methods in statistics and epidemiology. Recommendations from Epi-Aids led to policy implementation, evaluation, or modification. Epi-Aids provide the Centers for Disease Control and Prevention with the agility to respond rapidly to public health crises.
Epidemics in partially overlapped multiplex networks.
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Camila Buono
Full Text Available Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a different topology. In real-world networks, however, not all nodes are present on every layer. To generate a more realistic scenario, we use a generalized multiplex network and assume that only a fraction [Formula: see text] of the nodes are shared by the layers. We develop a theoretical framework for a branching process to describe the spread of an epidemic on these partially overlapped multiplex networks. This allows us to obtain the fraction of infected individuals as a function of the effective probability that the disease will be transmitted [Formula: see text]. We also theoretically determine the dependence of the epidemic threshold on the fraction [Formula: see text] of shared nodes in a system composed of two layers. We find that in the limit of [Formula: see text] the threshold is dominated by the layer with the smaller isolated threshold. Although a system of two completely isolated networks is nearly indistinguishable from a system of two networks that share just a few nodes, we find that the presence of these few shared nodes causes the epidemic threshold of the isolated network with the lower propagating capacity to change discontinuously and to acquire the threshold of the other network.
Spatiotemporal Analysis of the 2014 Ebola Epidemic in West Africa.
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Jantien A Backer
2016-12-01
Full Text Available In 2014-2016, Guinea, Sierra Leone and Liberia in West Africa experienced the largest and longest Ebola epidemic since the discovery of the virus in 1976. During the epidemic, incidence data were collected and published at increasing resolution. To monitor the epidemic as it spread within and between districts, we develop an analysis method that exploits the full spatiotemporal resolution of the data by combining a local model for time-varying effective reproduction numbers with a gravity-type model for spatial dispersion of the infection. We test this method in simulations and apply it to the weekly incidences of confirmed and probable cases per district up to June 2015, as reported by the World Health Organization. Our results indicate that, of the newly infected cases, only a small percentage, between 4% and 10%, migrates to another district, and a minority of these migrants, between 0% and 23%, leave their country. The epidemics in the three countries are found to be similar in estimated effective reproduction numbers, and in the probability of importing infection into a district. The countries might have played different roles in cross-border transmissions, although a sensitivity analysis suggests that this could also be related to underreporting. The spatiotemporal analysis method can exploit available longitudinal incidence data at different geographical locations to monitor local epidemics, determine the extent of spatial spread, reveal the contribution of local and imported cases, and identify sources of introductions in uninfected areas. With good quality data on incidence, this data-driven method can help to effectively control emerging infections.
Bayesian projection of life expectancy accounting for the HIV/AIDS epidemic
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Jessica Godwin
2017-11-01
Full Text Available Background: While probabilistic projection methods for projecting life expectancy exist, few account for covariates related to life expectancy. Generalized HIV/AIDS epidemics have a large, immediate negative impact on the life expectancy in a country, but this impact can be mitigated by widespread use of antiretroviral therapy (ART. Thus, projection methods for countries with generalized HIV/AIDS epidemics could be improved by accounting for HIV prevalence, the future course of the epidemic, and ART coverage. Methods: We extend the current Bayesian probabilistic life expectancy projection methods of Raftery et al. (2013 to account for HIV prevalence and adult ART coverage in countries with generalized HIV/AIDS epidemics. Results: We evaluate our method using out-of-sample validation. We ﬁnd that the proposed method performs better than the method that does not account for HIV prevalence or ART coverage for projections of life expectancy in countries with a generalized epidemic, while projections for countries without an epidemic remain essentially unchanged. Conclusions: In general, our projections show rapid recovery to pre-epidemic life expectancy levels in the presence of widespread ART coverage. After the initial life expectancy recovery, we project a steady rise in life expectancy until the end of the century. Contribution: We develop a simple Bayesian hierarchical model for long-term projections of life expectancy while accounting for HIV/AIDS prevalence and coverage of ART. The method produces well-calibrated projections for countries with generalized HIV/AIDS epidemics up to 2100 while having limited data demands.
Reverse-feeding effect of epidemic by propagators in two-layered networks
International Nuclear Information System (INIS)
Wu Dayu; Zhao Yanping; Zheng Muhua; Zhou Jie; Liu Zonghua
2016-01-01
Epidemic spreading has been studied for a long time and is currently focused on the spreading of multiple pathogens, especially in multiplex networks. However, little attention has been paid to the case where the mutual influence between different pathogens comes from a fraction of epidemic propagators, such as bisexual people in two separated groups of heterosexual and homosexual people. We here study this topic by presenting a network model of two layers connected by impulsive links, in contrast to the persistent links in each layer. We let each layer have a distinct pathogen and their interactive infection is implemented by a fraction of propagators jumping between the corresponding pairs of nodes in the two layers. By this model we show that (i) the propagators take the key role to transmit pathogens from one layer to the other, which significantly influences the stabilized epidemics; (ii) the epidemic thresholds will be changed by the propagators; and (iii) a reverse-feeding effect can be expected when the infective rate is smaller than its threshold of isolated spreading. A theoretical analysis is presented to explain the numerical results. (paper)
Extinction times of epidemic outbreaks in networks.
Holme, Petter
2013-01-01
In the Susceptible-Infectious-Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the population. Infections that are not contagious enough die out before they spread to a large fraction of people. We characterize how the maximal extinction time in SIR simulations on networks depend on the network structure. For example we find that the average distances in isolated components, weighted by the component size, is a good predictor of the maximal time to extinction. Furthermore, the transmission probability giving the longest outbreaks is larger than, but otherwise seemingly independent of, the epidemic threshold.
Extinction times of epidemic outbreaks in networks.
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Petter Holme
Full Text Available In the Susceptible-Infectious-Recovered (SIR model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the population. Infections that are not contagious enough die out before they spread to a large fraction of people. We characterize how the maximal extinction time in SIR simulations on networks depend on the network structure. For example we find that the average distances in isolated components, weighted by the component size, is a good predictor of the maximal time to extinction. Furthermore, the transmission probability giving the longest outbreaks is larger than, but otherwise seemingly independent of, the epidemic threshold.
Frameworks for understanding and describing business models
DEFF Research Database (Denmark)
Nielsen, Christian; Roslender, Robin
2014-01-01
This chapter provides in a chronological fashion an introduction to six frameworks that one can apply to describing, understanding and also potentially innovating business models. These six frameworks have been chosen carefully as they represent six very different perspectives on business models...... and in this manner “complement” each other. There are a multitude of varying frameworks that could be chosen from and we urge the reader to search and trial these for themselves. The six chosen models (year of release in parenthesis) are: • Service-Profit Chain (1994) • Strategic Systems Auditing (1997) • Strategy...... Maps (2001) • Intellectual Capital Statements (2003) • Chesbrough’s framework for Open Business Models (2006) • Business Model Canvas (2008)...
Networked SIS Epidemics With Awareness
Paarporn, Keith; Eksin, Ceyhun; Weitz, Joshua S.; Shamma, Jeff S.
2017-01-01
We study a susceptible-infected-susceptible epidemic process over a static contact network where the nodes have partial information about the epidemic state. They react by limiting their interactions with their neighbors when they believe
Effects of human dynamics on epidemic spreading in Côte d'Ivoire
Li, Ruiqi; Wang, Wenxu; Di, Zengru
2017-02-01
Understanding and predicting outbreaks of contagious diseases are crucial to the development of society and public health, especially for underdeveloped countries. However, challenging problems are encountered because of complex epidemic spreading dynamics influenced by spatial structure and human dynamics (including both human mobility and human interaction intensity). We propose a systematical model to depict nationwide epidemic spreading in Côte d'Ivoire, which integrates multiple factors, such as human mobility, human interaction intensity, and demographic features. We provide insights to aid in modeling and predicting the epidemic spreading process by data-driven simulation and theoretical analysis, which is otherwise beyond the scope of local evaluation and geometrical views. We show that the requirement that the average local basic reproductive number to be greater than unity is not necessary for outbreaks of epidemics. The observed spreading phenomenon can be roughly explained as a heterogeneous diffusion-reaction process by redefining mobility distance according to the human mobility volume between nodes, which is beyond the geometrical viewpoint. However, the heterogeneity of human dynamics still poses challenges to precise prediction.
Predicting epidemic outbreak from individual features of the spreaders
International Nuclear Information System (INIS)
Da Silva, Renato Aparecido Pimentel; Viana, Matheus Palhares; Da Fontoura Costa, Luciano
2012-01-01
Knowing which individuals can be more efficient in spreading a pathogen throughout a determinate environment is a fundamental question in disease control. Indeed, over recent years the spread of epidemic diseases and its relationship with the topology of the involved system have been a recurrent topic in complex network theory, taking into account both network models and real-world data. In this paper we explore possible correlations between the heterogeneous spread of an epidemic disease governed by the susceptible–infected–recovered (SIR) model, and several attributes of the originating vertices, considering Erdös–Rényi (ER), Barabási–Albert (BA) and random geometric graphs (RGG), as well as a real case study, the US air transportation network, which comprises the 500 busiest airports in the US along with inter-connections. Initially, the heterogeneity of the spreading is achieved by considering the RGG networks, in which we analytically derive an expression for the distribution of the spreading rates among the established contacts, by assuming that such rates decay exponentially with the distance that separates the individuals. Such a distribution is also considered for the ER and BA models, where we observe topological effects on the correlations. In the case of the airport network, the spreading rates are empirically defined, assumed to be directly proportional to the seat availability. Among both the theoretical and real networks considered, we observe a high correlation between the total epidemic prevalence and the degree, as well as the strength and the accessibility of the epidemic sources. For attributes such as the betweenness centrality and the k-shell index, however, the correlation depends on the topology considered. (paper)
Dynamics and optimal control of a non-linear epidemic model with relapse and cure
Lahrouz, A.; El Mahjour, H.; Settati, A.; Bernoussi, A.
2018-04-01
In this work, we introduce the basic reproduction number R0 for a general epidemic model with graded cure, relapse and nonlinear incidence rate in a non-constant population size. We established that the disease free-equilibrium state Ef is globally asymptotically exponentially stable if R0 1, we proved that the system model has at least one endemic state Ee. Then, by means of an appropriate Lyapunov function, we showed that Ee is unique and globally asymptotically stable under some acceptable biological conditions. On the other hand, we use two types of control to reduce the number of infectious individuals. The optimality system is formulated and solved numerically using a Gauss-Seidel-like implicit finite-difference method.
Mean field theory of epidemic spreading with effective contacts on networks
International Nuclear Information System (INIS)
Wu, Qingchu; Chen, Shufang
2015-01-01
We present a general approach to the analysis of the susceptible-infected-susceptible model with effective contacts on networks, where each susceptible node will be infected with a certain probability only for effective contacts. In the network, each node has a given effective contact number. By using the one-vertex heterogenous mean-field (HMF) approximation and the pair HMF approximation, we obtain conditions for epidemic outbreak on degree-uncorrelated networks. Our results suggest that the epidemic threshold is closely related to the effective contact and its distribution. However, when the effective contact is only dependent of node degree, the epidemic threshold can be established by the degree distribution of networks.
Statistical models describing the energy signature of buildings
DEFF Research Database (Denmark)
Bacher, Peder; Madsen, Henrik; Thavlov, Anders
2010-01-01
Approximately one third of the primary energy production in Denmark is used for heating in buildings. Therefore efforts to accurately describe and improve energy performance of the building mass are very important. For this purpose statistical models describing the energy signature of a building, i...... or varying energy prices. The paper will give an overview of statistical methods and applied models based on experiments carried out in FlexHouse, which is an experimental building in SYSLAB, Risø DTU. The models are of different complexity and can provide estimates of physical quantities such as UA......-values, time constants of the building, and other parameters related to the heat dynamics. A method for selecting the most appropriate model for a given building is outlined and finally a perspective of the applications is given. Aknowledgements to the Danish Energy Saving Trust and the Interreg IV ``Vind i...
An individual-based approach to SIR epidemics in contact networks.
Youssef, Mina; Scoglio, Caterina
2011-08-21
Many approaches have recently been proposed to model the spread of epidemics on networks. For instance, the Susceptible/Infected/Recovered (SIR) compartmental model has successfully been applied to different types of diseases that spread out among humans and animals. When this model is applied on a contact network, the centrality characteristics of the network plays an important role in the spreading process. However, current approaches only consider an aggregate representation of the network structure, which can result in inaccurate analysis. In this paper, we propose a new individual-based SIR approach, which considers the whole description of the network structure. The individual-based approach is built on a continuous time Markov chain, and it is capable of evaluating the state probability for every individual in the network. Through mathematical analysis, we rigorously confirm the existence of an epidemic threshold below which an epidemic does not propagate in the network. We also show that the epidemic threshold is inversely proportional to the maximum eigenvalue of the network. Additionally, we study the role of the whole spectrum of the network, and determine the relationship between the maximum number of infected individuals and the set of eigenvalues and eigenvectors. To validate our approach, we analytically study the deviation with respect to the continuous time Markov chain model, and we show that the new approach is accurate for a large range of infection strength. Furthermore, we compare the new approach with the well-known heterogeneous mean field approach in the literature. Ultimately, we support our theoretical results through extensive numerical evaluations and Monte Carlo simulations. Published by Elsevier Ltd.
Righetto, L.; Bertuzzo, E.; Mari, L.; Casagrandi, R.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.
2012-12-01
Following the acknowledgement of a clear correlation between rainfall events and cholera resurgence, that was observed in Haiti starting from May 2011, we use a multi-variate Poisson generator to produce rainfall inputs, with which we force spatially explicit models of cholera spreading. Our models consist of ODE systems of equations, describing a network of human communities (divided in Susceptible, Infected and Recovered individuals) connected by river transport of pathogens and human mobility. We perform an a posteriori analysis -- from the beginning of the epidemic until December 2011 -- to assess the model reliability in predicting cholera cases and in testing control measures -- involving vaccination and sanitation campaigns. We then run a multi-seasonal prediction of the course of the epidemic until December 2015, to investigate further resurgences of cholera in the region and to evaluate, again, the effect of policies which may bring to the eradication of the disease in Haiti. We conclude that mathematical models may represent a key information tool for policy makers, as a way to preliminarly assess the possible future course of an epidemic and to test intervention policies to be deployed. Effect of intervention policies on the predicted course of the epidemic between 28/05-31/12/2011 (blue lines: simulations with the observed rainfall pattern; red lines/shaded range: median/25th-75th percentile range of simulations with generated rainfall). A) Effect of a reduction of the 20% of the contact rate , applied in one month starting from the 1st of June (dashed blue/red lines) or the 1st of July (dotted blue/red lines). B) A) Effect of a vaccination of 4 million individuals, implemented in one month starting from the 1st of June (dashed blue/red lines) or the 1st of July (dotted blue/red lines). C) Number of new cases in the period 28/05-31/12/2011 as a function of the reduction of the contact rate . D) Number of new cases in the period 28/05-31/12/2011 as a
Optimal control of information epidemics modeled as Maki Thompson rumors
Kandhway, Kundan; Kuri, Joy
2014-12-01
We model the spread of information in a homogeneously mixed population using the Maki Thompson rumor model. We formulate an optimal control problem, from the perspective of single campaigner, to maximize the spread of information when the campaign budget is fixed. Control signals, such as advertising in the mass media, attempt to convert ignorants and stiflers into spreaders. We show the existence of a solution to the optimal control problem when the campaigning incurs non-linear costs under the isoperimetric budget constraint. The solution employs Pontryagin's Minimum Principle and a modified version of forward backward sweep technique for numerical computation to accommodate the isoperimetric budget constraint. The techniques developed in this paper are general and can be applied to similar optimal control problems in other areas. We have allowed the spreading rate of the information epidemic to vary over the campaign duration to model practical situations when the interest level of the population in the subject of the campaign changes with time. The shape of the optimal control signal is studied for different model parameters and spreading rate profiles. We have also studied the variation of the optimal campaigning costs with respect to various model parameters. Results indicate that, for some model parameters, significant improvements can be achieved by the optimal strategy compared to the static control strategy. The static strategy respects the same budget constraint as the optimal strategy and has a constant value throughout the campaign horizon. This work finds application in election and social awareness campaigns, product advertising, movie promotion and crowdfunding campaigns.
Dynamic properties of epidemic spreading on finite size complex networks
Li, Ying; Liu, Yang; Shan, Xiu-Ming; Ren, Yong; Jiao, Jian; Qiu, Ben
2005-11-01
The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS (susceptible-infected-susceptible) model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.
Context analysis for epidemic control in the Netherlands
Huizer, Y.L.; Kraaij-Dirkzwager, M.M.; Timen, A.; Schuitmaker-Warnaar, T.J.; van Steenbergen, J.E.
2014-01-01
When epidemics occur, experts advise the Ministries on effective control measures. There is uncertainty in the translation of epidemiological evidence into effective outbreak management interventions, due to contradicatory problem perspectives, diverse interests and time pressure. Several models
Dennis, Ann M.; Herbeck, Joshua T.; Brown, Andrew Leigh; Kellam, Paul; de Oliveira, Tulio; Pillay, Deenan; Fraser, Christophe; Cohen, Myron S.
2014-01-01
Efficient and effective HIV prevention measures for generalized epidemics in sub-Saharan Africa have not yet been validated at the population-level. Design and impact evaluation of such measures requires fine-scale understanding of local HIV transmission dynamics. The novel tools of HIV phylogenetics and molecular epidemiology may elucidate these transmission dynamics. Such methods have been incorporated into studies of concentrated HIV epidemics to identify proximate and determinant traits associated with ongoing transmission. However, applying similar phylogenetic analyses to generalized epidemics, including the design and evaluation of prevention trials, presents additional challenges. Here we review the scope of these methods and present examples of their use in concentrated epidemics in the context of prevention. Next, we describe the current uses for phylogenetics in generalized epidemics, and discuss their promise for elucidating transmission patterns and informing prevention trials. Finally, we review logistic and technical challenges inherent to large-scale molecular epidemiological studies of generalized epidemics, and suggest potential solutions. PMID:24977473
On the existence of a threshold for preventive behavioral responses to suppress epidemic spreading.
Sahneh, Faryad Darabi; Chowdhury, Fahmida N; Scoglio, Caterina M
2012-01-01
The spontaneous behavioral responses of individuals to the progress of an epidemic are recognized to have a significant impact on how the infection spreads. One observation is that, even if the infection strength is larger than the classical epidemic threshold, the initially growing infection can diminish as the result of preventive behavioral patterns adopted by the individuals. In order to investigate such dynamics of the epidemic spreading, we use a simple behavioral model coupled with the individual-based SIS epidemic model where susceptible individuals adopt a preventive behavior when sensing infection. We show that, given any infection strength and contact topology, there exists a region in the behavior-related parameter space such that infection cannot survive in long run and is completely contained. Several simulation results, including a spreading scenario in a realistic contact network from a rural district in the State of Kansas, are presented to support our analytical arguments.
[Epidemic parotiditis, a reportable disease].
Boverhoff, J C; Baart, J A
2013-01-01
Three consecutive patients with an acute swelling of one of the cheeks, were diagnosed with epidemic parotiditis. The first phase of the diagnostic procedure for an acute cheek swelling is to eliminate the possibility of odontogenic causes. When odontogenic problems have been excluded, non-dentition-related causes may be considered. An acute, progressive swelling in the preauricular area can often be attributed to an inflammation of the parotid gland, but epidemic parotiditis should also be considered. Epidemic parotiditis, or mumps, is caused by the mumps virus. Contamination occurs aerogenically. In the Netherlands, mumps vaccine is an ingredient of the governmental combined mump-measles-rubella inoculation programme. However, in recent years several small-scale parotiditis epidemics have broken out, predominantly among young, inoculated adults. Oropharyngeal mucus and blood samples are needed to diagnose the disease. Each case of the disease should be reported to the community healthcare service.
Concurrency can drive an HIV epidemic by moving R0 across the epidemic threshold
Leung, Ka Yin; Kretzschmar, Mirjam
2015-01-01
OBJECTIVE: The objective of this study is to investigate whether concurrency can drive an HIV epidemic by moving R0 across the epidemic threshold. DESIGN AND METHODS: We use a mathematical framework for a dynamic partnership network and the spread of a one-stage infection to study how concurrency is
Influence of Media on Seasonal Influenza Epidemic Curves.
Saito, Satoshi; Saito, Norihiro; Itoga, Masamichi; Ozaki, Hiromi; Kimura, Toshiyuki; Okamura, Yuji; Murakami, Hiroshi; Kayaba, Hiroyuki
2016-09-01
Theoretical investigations predicting the epidemic curves of seasonal influenza have been demonstrated so far; however, there is little empirical research using ever accumulated epidemic curves. The effects of vaccine coverage and information distribution on influenza epidemics were evaluated. Four indices for epidemics (i.e., onset-peak duration, onset-end duration, ratio of the onset-peak duration to onset-end duration and steepness of epidemic curves) were defined, and the correlations between these indices and anti-flu drug prescription dose, vaccine coverage, the volume of media and search trend on influenza through internet were analyzed. Epidemiological data on seasonal influenza epidemics from 2002/2003 to 2013/2014 excluding 2009/2010 season were collected from National Institute of Infectious Diseases of Japan. The onset-peak duration and its ratio to onset-end duration correlated inversely with the volume of anti-flu drug prescription. Onset-peak duration correlated positively with media information volume on influenza. The steepness of the epidemic curve, and anti-flu drug prescription dose inversely correlated with the volume of media information. Pre-epidemic search trend and media volume on influenza correlated with the vaccine coverage in the season. Vaccine coverage had no strong effect on epidemic curve. Education through media has an effect on the epidemic curve of seasonal influenza. Copyright © 2016 The Author(s). Published by Elsevier Ltd.. All rights reserved.
The global spread of HIV-1 subtype B epidemic.
Magiorkinis, Gkikas; Angelis, Konstantinos; Mamais, Ioannis; Katzourakis, Aris; Hatzakis, Angelos; Albert, Jan; Lawyer, Glenn; Hamouda, Osamah; Struck, Daniel; Vercauteren, Jurgen; Wensing, Annemarie; Alexiev, Ivailo; Åsjö, Birgitta; Balotta, Claudia; Gomes, Perpétua; Camacho, Ricardo J; Coughlan, Suzie; Griskevicius, Algirdas; Grossman, Zehava; Horban, Anders; Kostrikis, Leondios G; Lepej, Snjezana J; Liitsola, Kirsi; Linka, Marek; Nielsen, Claus; Otelea, Dan; Paredes, Roger; Poljak, Mario; Puchhammer-Stöckl, Elizabeth; Schmit, Jean Claude; Sönnerborg, Anders; Staneková, Danica; Stanojevic, Maja; Stylianou, Dora C; Boucher, Charles A B; Nikolopoulos, Georgios; Vasylyeva, Tetyana; Friedman, Samuel R; van de Vijver, David; Angarano, Gioacchino; Chaix, Marie-Laure; de Luca, Andrea; Korn, Klaus; Loveday, Clive; Soriano, Vincent; Yerly, Sabine; Zazzi, Mauricio; Vandamme, Anne-Mieke; Paraskevis, Dimitrios
2016-12-01
Human immunodeficiency virus type 1 (HIV-1) was discovered in the early 1980s when the virus had already established a pandemic. For at least three decades the epidemic in the Western World has been dominated by subtype B infections, as part of a sub-epidemic that traveled from Africa through Haiti to United States. However, the pattern of the subsequent spread still remains poorly understood. Here we analyze a large dataset of globally representative HIV-1 subtype B strains to map their spread around the world over the last 50years and describe significant spread patterns. We show that subtype B travelled from North America to Western Europe in different occasions, while Central/Eastern Europe remained isolated for the most part of the early epidemic. Looking with more detail in European countries we see that the United Kingdom, France and Switzerland exchanged viral isolates with non-European countries than with European ones. The observed pattern is likely to mirror geopolitical landmarks in the post-World War II era, namely the rise and the fall of the Iron Curtain and the European colonialism. In conclusion, HIV-1 spread through specific migration routes which are consistent with geopolitical factors that affected human activities during the last 50years, such as migration, tourism and trade. Our findings support the argument that epidemic control policies should be global and incorporate political and socioeconomic factors. Copyright Â© 2016 The Authors. Published by Elsevier B.V. All rights reserved.
Guo, Dongmin; Li, King C; Peters, Timothy R; Snively, Beverly M; Poehling, Katherine A; Zhou, Xiaobo
2015-03-11
Mathematical modeling of influenza epidemic is important for analyzing the main cause of the epidemic and finding effective interventions towards it. The epidemic is a dynamic process. In this process, daily infections are caused by people's contacts, and the frequency of contacts can be mainly influenced by their cognition to the disease. The cognition is in turn influenced by daily illness attack rate, climate, and other environment factors. Few existing methods considered the dynamic process in their models. Therefore, their prediction results can hardly be explained by the mechanisms of epidemic spreading. In this paper, we developed a heterogeneous graph modeling approach (HGM) to describe the dynamic process of influenza virus transmission by taking advantage of our unique clinical data. We built social network of studied region and embedded an Agent-Based Model (ABM) in the HGM to describe the dynamic change of an epidemic. Our simulations have a good agreement with clinical data. Parameter sensitivity analysis showed that temperature influences the dynamic of epidemic significantly and system behavior analysis showed social network degree is a critical factor determining the size of an epidemic. Finally, multiple scenarios for vaccination and school closure strategies were simulated and their performance was analyzed.
Ebola epidemic--Liberia, March-October 2014.
Nyenswah, Tolbert; Fahnbulleh, Miatta; Massaquoi, Moses; Nagbe, Thomas; Bawo, Luke; Falla, James Dorbor; Kohar, Henry; Gasasira, Alex; Nabeth, Pierre; Yett, Sheldon; Gergonne, Bernadette; Casey, Sean; Espinosa, Benjamin; McCoy, Andrea; Feldman, Heinz; Hensley, Lisa; Baily, Mark; Fields, Barry; Lo, Terrence; Lindblade, Kim; Mott, Josh; Boulanger, Lucy; Christie, Athalia; Wang, Susan; Montgomery, Joel; Mahoney, Frank
2014-11-21
On March 21, 2014, the Guinea Ministry of Health reported the outbreak of an illness characterized by fever, severe diarrhea, vomiting and a high fatality rate (59%), leading to the first known epidemic of Ebola virus disease (Ebola) in West Africa and the largest and longest Ebola epidemic in history. As of November 2, Liberia had reported the largest number of cases (6,525) and deaths (2,697) among the three affected countries of West Africa with ongoing transmission (Guinea, Liberia, and Sierra Leone). The response strategy in Liberia has included management of the epidemic through an incident management system (IMS) in which the activities of all partners are coordinated. Within the IMS, key strategies for epidemic control include surveillance, case investigation, laboratory confirmation, contact tracing, safe transportation of persons with suspected Ebola, isolation, infection control within the health care system, community engagement, and safe burial. This report provides a brief overview of the progression of the epidemic in Liberia and summarizes the interventions implemented.
Reverse-feeding effect of epidemic by propagators in two-layered networks
Dayu, Wu; Yanping, Zhao; Muhua, Zheng; Jie, Zhou; Zonghua, Liu
2016-02-01
Epidemic spreading has been studied for a long time and is currently focused on the spreading of multiple pathogens, especially in multiplex networks. However, little attention has been paid to the case where the mutual influence between different pathogens comes from a fraction of epidemic propagators, such as bisexual people in two separated groups of heterosexual and homosexual people. We here study this topic by presenting a network model of two layers connected by impulsive links, in contrast to the persistent links in each layer. We let each layer have a distinct pathogen and their interactive infection is implemented by a fraction of propagators jumping between the corresponding pairs of nodes in the two layers. By this model we show that (i) the propagators take the key role to transmit pathogens from one layer to the other, which significantly influences the stabilized epidemics; (ii) the epidemic thresholds will be changed by the propagators; and (iii) a reverse-feeding effect can be expected when the infective rate is smaller than its threshold of isolated spreading. A theoretical analysis is presented to explain the numerical results. Project supported by the National Natural Science Foundation of China (Grant Nos. 11135001, 11375066, and 11405059) and the National Basic Key Program of China (Grant No. 2013CB834100).
Mathematical and statistical modeling for emerging and re-emerging infectious diseases
Hyman, James
2016-01-01
The contributions by epidemic modeling experts describe how mathematical models and statistical forecasting are created to capture the most important aspects of an emerging epidemic.Readers will discover a broad range of approaches to address questions, such as Can we control Ebola via ring vaccination strategies? How quickly should we detect Ebola cases to ensure epidemic control? What is the likelihood that an Ebola epidemic in West Africa leads to secondary outbreaks in other parts of the world? When does it matter to incorporate the role of disease-induced mortality on epidemic models? What is the role of behavior changes on Ebola dynamics? How can we better understand the control of cholera or Ebola using optimal control theory? How should a population be structured in order to mimic the transmission dynamics of diseases such as chlamydia, Ebola, or cholera? How can we objectively determine the end of an epidemic? How can we use metapopulation models to understand the role of movement restrictions and mi...
The protection against infection and epidemics as a point of the disaster-related medicine
International Nuclear Information System (INIS)
Stickl, H.
1981-01-01
If the hygienic infrastructure is maintained, epidemics cannot reach the extent of a catastrophe. During the course of a catastrophe, however, epidemics can develop; they may accompany and influence the outcome of a catastrophe. This can take place if the hygienic infrastructure is disturbed or destroyed, or if the resistance of the affected population is impaired (intoxication, hunger, irradiation, etc.). Proven an possible remedies and methods to prevent the infections consequences of catastrophes are described. (orig.) [de
Homo-psychologicus: Reactionary behavioural aspects of epidemics
Alhaji Cherif; Kamal Barley; Marcel Hurtado
2016-01-01
We formulate an in silico model of pathogen avoidance mechanism and investigate its impact on defensive behavioural measures (e.g., spontaneous social exclusions and distancing, crowd avoidance and voluntary vaccination adaptation). In particular, we use SIR(B)S (e.g., susceptible-infected-recovered with additional behavioural component) model to investigate the impact of homo-psychologicus aspects of epidemics. We focus on reactionary behavioural changes, which apply to both social distancin...
Heightened vulnerability to MDR-TB epidemics after controlling drug-susceptible TB.
Directory of Open Access Journals (Sweden)
Jason D Bishai
2010-09-01
Full Text Available Prior infection with one strain TB has been linked with diminished likelihood of re-infection by a new strain. This paper attempts to determine the role of declining prevalence of drug-susceptible TB in enabling future epidemics of MDR-TB.A computer simulation of MDR-TB epidemics was developed using an agent-based model platform programmed in NetLogo (See http://mdr.tbtools.org/. Eighty-one scenarios were created, varying levels of treatment quality, diagnostic accuracy, microbial fitness cost, and the degree of immunogenicity elicited by drug-susceptible TB. Outcome measures were the number of independent MDR-TB cases per trial and the proportion of trials resulting in MDR-TB epidemics for a 500 year period after drug therapy for TB is introduced.MDR-TB epidemics propagated more extensively after TB prevalence had fallen. At a case detection rate of 75%, improving therapeutic compliance from 50% to 75% can reduce the probability of an epidemic from 45% to 15%. Paradoxically, improving the case-detection rate from 50% to 75% when compliance with DOT is constant at 75% increases the probability of MDR-TB epidemics from 3% to 45%.The ability of MDR-TB to spread depends on the prevalence of drug-susceptible TB. Immunologic protection conferred by exposure to drug-susceptible TB can be a crucial factor that prevents MDR-TB epidemics when TB treatment is poor. Any single population that successfully reduces its burden of drug-susceptible TB will have reduced herd immunity to externally or internally introduced strains of MDR-TB and can experience heightened vulnerability to an epidemic. Since countries with good TB control may be more vulnerable, their self interest dictates greater promotion of case detection and DOTS implementation in countries with poor control to control their risk of MDR-TB.
Contact allergy epidemics and their controls
DEFF Research Database (Denmark)
Thyssen, Jacob Pontoppidan; Johansen, Jeanne Duus; Menné, Torkil
2007-01-01
Contact dermatitis can be severe and lead to sick leave as well as significant healthcare expenses. The aim of this review is to present the published knowledge on 6 historical epidemics of contact allergy to apply this knowledge on the prevention and control of future contact allergy epidemics. ...... to prevent contact allergy epidemics. It is essential that dermatologist, scientists, administrators, and consumers organize and structure known methods to accelerate the control of emerging contact allergens....
Epidemics in Ming and Qing China: Impacts of changes of climate and economic well-being.
Pei, Qing; Zhang, David D; Li, Guodong; Winterhalder, Bruce; Lee, Harry F
2015-07-01
We investigated the mechanism of epidemics with the impacts of climate change and socio-economic fluctuations in the Ming and Qing Dynasties in China (AD 1368-1901). Using long-term and high-quality datasets, this study is the first quantitative research that verifies the 'climate change → economy → epidemics' mechanism in historical China by statistical methods that include correlation analysis, Granger causality analysis, ARX, and Poisson-ARX modeling. The analysis provides the evidences that climate change could only fundamentally lead to the epidemics spread and occurrence, but the depressed economic well-being is the direct trigger of epidemics spread and occurrence at the national and long term scale in historical China. Moreover, statistical modeling shows that economic well-being is more important than population pressure in the mechanism of epidemics. However, population pressure remains a key element in determining the social vulnerability of the epidemics occurrence under climate change. Notably, the findings not only support adaptation theories but also enhance our confidence to address climatic shocks if economic buffering capacity can be promoted steadily. The findings can be a basis for scientists and policymakers in addressing global and regional environmental changes. Copyright © 2015 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Sharmistha Mishra
Full Text Available To design HIV prevention programmes, it is critical to understand the temporal and geographic aspects of the local epidemic and to address the key behaviours that drive HIV transmission. Two methods have been developed to appraise HIV epidemics and guide prevention strategies. The numerical proxy method classifies epidemics based on current HIV prevalence thresholds. The Modes of Transmission (MOT model estimates the distribution of incidence over one year among risk-groups. Both methods focus on the current state of an epidemic and provide short-term metrics which may not capture the epidemiologic drivers. Through a detailed analysis of country and sub-national data, we explore the limitations of the two traditional methods and propose an alternative approach.We compared outputs of the traditional methods in five countries for which results were published, and applied the numeric and MOT model to India and six districts within India. We discovered three limitations of the current methods for epidemic appraisal: (1 their results failed to identify the key behaviours that drive the epidemic; (2 they were difficult to apply to local epidemics with heterogeneity across district-level administrative units; and (3 the MOT model was highly sensitive to input parameters, many of which required extraction from non-regional sources. We developed an alternative decision-tree framework for HIV epidemic appraisals, based on a qualitative understanding of epidemiologic drivers, and demonstrated its applicability in India. The alternative framework offered a logical algorithm to characterize epidemics; it required minimal but key data.Traditional appraisals that utilize the distribution of prevalent and incident HIV infections in the short-term could misguide prevention priorities and potentially impede efforts to halt the trajectory of the HIV epidemic. An approach that characterizes local transmission dynamics provides a potentially more effective tool with
Directory of Open Access Journals (Sweden)
Matthias An der Heiden
Full Text Available BACKGROUND: On June 11, 2009, the World Health Organization declared phase 6 of the novel influenza A/H1N1 pandemic. Although by the end of September 2009, the novel virus had been reported from all continents, the impact in most countries of the northern hemisphere has been limited. The return of the virus in a second wave would encounter populations that are still nonimmune and not vaccinated yet. We modelled the effect of control strategies to reduce the spread with the goal to defer the epidemic wave in a country where it is detected in a very early stage. METHODOLOGY/PRINCIPAL FINDINGS: We constructed a deterministic SEIR model using the age distribution and size of the population of Germany based on the observed number of imported cases and the early findings for the epidemiologic characteristics described by Fraser (Science, 2009. We propose a two-step control strategy with an initial effort to trace, quarantine, and selectively give prophylactic treatment to contacts of the first 100 to 500 cases. In the second step, the same measures are focused on the households of the next 5,000 to 10,000 cases. As a result, the peak of the epidemic could be delayed up to 7.6 weeks if up to 30% of cases are detected. However, the cumulative attack rates would not change. Necessary doses of antivirals would be less than the number of treatment courses for 0.1% of the population. In a sensitivity analysis, both case detection rate and the variation of R0 have major effects on the resulting delay. CONCLUSIONS/SIGNIFICANCE: Control strategies that reduce the spread of the disease during the early phase of a pandemic wave may lead to a substantial delay of the epidemic. Since prophylactic treatment is only offered to the contacts of the first 10,000 cases, the amount of antivirals needed is still very limited.
Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate
International Nuclear Information System (INIS)
Wang Zhi-Gang; Gao Rui-Mei; Fan Xiao-Ming; Han Qi-Xing
2014-01-01
We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ 0 , a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ 0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ 0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ 0 , when the stochastic system obeys some conditions and ℛ 0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations. (general)
[The depression epidemic does not exist].
van der Feltz-Cornelis, Christina M
2009-01-01
There has been much discussion in the media about the question of the existence of a depression epidemic. This leads on to the questions of whether the social and economic approaches are adequate, and what the alternatives are. The concept of the disease 'depression' can be defined using a medical model, or from a patient's or a societal perspective. From a medical perspective, indeed a depression epidemic has ensued from the increased prosperity and the associated decompression of the mortality rate. Society responded with preventative measures and policies aimed at improving functioning in the workplace. However, patients with a major depressive disorder (MDD) who are eligible for treatment are often not motivated to take it up, or are undertreated. Research is necessary in order to explore what patients think about the identification and treatment of depression. The confusion regarding the concept of depression found in the media, needs to be cleared.
Molecular Epidemiological Study of Mumps Epidemics of 2015 in Okinawa, Japan.
Kuba, Yumani; Kyan, Hisako; Arakaki, Eri; Takara, Taketoshi; Kato, Takashi; Okano, Sho; Oshiro, Yuko; Kudaka, Jun; Kidokoro, Minoru
2017-05-24
Although major mumps epidemics occurred every 4-5 years in Okinawa Prefecture in Japan, no laboratory diagnoses were conducted. A mumps epidemic started in Okinawa in October 2014, and we collected clinical samples from 31 patients in 4 areas (Hokubu, Nanbu, Miyako, and Yaeyama) from July to December 2015, for virus isolation and RT-PCR, whose positive ratios were 52% and 87%, respectively. Phylogenetic analyses showed that all isolates were classified into genotype G, and with one exception, consisted of 2 subgenotypes, Ge (55.6%) and Gw (40.7%), which have been prominent in Japan recently. One isolate was classified in another lineage, which was detected in Japan for the first time, and was similar to a Hong Kong isolate from 2014. Remarkably, the geographic distributions of the 2 major lineages were separated. The Ge viruses were isolated from the main island of Okinawa and the Yaeyama Islands, whereas the Gw isolates were mainly detected from the Miyako Islands. These results suggest that the Ge and Gw mumps viruses mainly caused the mumps epidemics of 2015 in Okinawa, and that they spread independently in separate regions. This is the first report describing the molecular epidemiology of mumps epidemics in Okinawa Prefecture.
Fluctuations and Noise in Stochastic Spread of Respiratory Infection Epidemics in Social Networks
Yulmetyev, Renat; Emelyanova, Natalya; Demin, Sergey; Gafarov, Fail; Hänggi, Peter; Yulmetyeva, Dinara
2003-05-01
For the analysis of epidemic and disease dynamics complexity, it is necessary to understand the basic principles and notions of its spreading in long-time memory media. Here we considering the problem from a theoretical and practical viewpoint, presenting the quantitative evidence confirming the existence of stochastic long-range memory and robust chaos in a real time series of respiratory infections of human upper respiratory track. In this work we present a new statistical method of analyzing the spread of grippe and acute respiratory track infections epidemic process of human upper respiratory track by means of the theory of discrete non-Markov stochastic processes. We use the results of our recent theory (Phys. Rev. E 65, 046107 (2002)) for the study of statistical effects of memory in real data series, describing the epidemic dynamics of human acute respiratory track infections and grippe. The obtained results testify to an opportunity of the strict quantitative description of the regular and stochastic components in epidemic dynamics of social networks with a view to time discreteness and effects of statistical memory.
The Social Impact of Communication during Epidemics: Bioethical and Public Health Perspectives
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Eduardo Alfredo Duro
2018-06-01
Full Text Available Public health communication and, especially during a crisis scenario such as an epidemics, is mediated by ethical conflicts ranging from values to deontology. In an intercommunicated world, the social support during outbreaks and epidemics becomes global and the state presence is a key to social protection. This should also be translated into timely, urgent and effective communication strategies from the public health perspective as well as efforts to prevent and avoid fake news or skewed information from any sources. Scenarios with lack of connection and obstacles in mass communication in public health major threats are described.
DEFF Research Database (Denmark)
Halasa, Tariq; Bøtner, Anette; Mortensen, Sten
2018-01-01
control an epidemic of ASF. A previously published and well documented simulation model for ASF virus spread between herds was used to examine the epidemiologic and economic impacts of the duration and size of the control zones around affected herds. In the current study, scenarios were run, where......African swine fever (ASF) is a notifiable infectious disease. The disease is endemic in certain regions in Eastern Europe constituting a risk of ASF spread toward Western Europe. Therefore, as part of contingency planning, it is important to continuously explore strategies that can effectively...... or clinical and serological surveillance of herds within the zones. Sensitivity analysis was conducted on influential input parameters in the model. The model predicts that reducing the duration of the protection and surveillance zones has no impact on the epidemiological consequences of the epidemics, while...
Random migration processes between two stochastic epidemic centers.
Sazonov, Igor; Kelbert, Mark; Gravenor, Michael B
2016-04-01
We consider the epidemic dynamics in stochastic interacting population centers coupled by random migration. Both the epidemic and the migration processes are modeled by Markov chains. We derive explicit formulae for the probability distribution of the migration process, and explore the dependence of outbreak patterns on initial parameters, population sizes and coupling parameters, using analytical and numerical methods. We show the importance of considering the movement of resident and visitor individuals separately. The mean field approximation for a general migration process is derived and an approximate method that allows the computation of statistical moments for networks with highly populated centers is proposed and tested numerically. Copyright © 2016 Elsevier Inc. All rights reserved.
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Luque Fernandez Miguel A
2012-06-01
Full Text Available Abstract Background In highly populated African urban areas where access to clean water is a challenge, water source contamination is one of the most cited risk factors in a cholera epidemic. During the rainy season, where there is either no sewage disposal or working sewer system, runoff of rains follows the slopes and gets into the lower parts of towns where shallow wells could easily become contaminated by excretes. In cholera endemic areas, spatial information about topographical elevation could help to guide preventive interventions. This study aims to analyze the association between topographic elevation and the distribution of cholera cases in Harare during the cholera epidemic in 2008 and 2009. Methods We developed an ecological study using secondary data. First, we described attack rates by suburb and then calculated rate ratios using whole Harare as reference. We illustrated the average elevation and cholera cases by suburbs using geographical information. Finally, we estimated a generalized linear mixed model (under the assumption of a Poisson distribution with an Empirical Bayesian approach to model the relation between the risk of cholera and the elevation in meters in Harare. We used a random intercept to allow for spatial correlation of neighboring suburbs. Results This study identifies a spatial pattern of the distribution of cholera cases in the Harare epidemic, characterized by a lower cholera risk in the highest elevation suburbs of Harare. The generalized linear mixed model showed that for each 100 meters of increase in the topographical elevation, the cholera risk was 30% lower with a rate ratio of 0.70 (95% confidence interval=0.66-0.76. Sensitivity analysis confirmed the risk reduction with an overall estimate of the rate ratio between 20% and 40%. Conclusion This study highlights the importance of considering topographical elevation as a geographical and environmental risk factor in order to plan cholera preventive
Defining and detecting malaria epidemics in south-east Iran.
McKelvie, William R; Haghdoost, Ali Akbar; Raeisi, Ahmad
2012-03-23
A lack of consensus on how to define malaria epidemics has impeded the evaluation of early detection systems. This study aimed to develop local definitions of malaria epidemics in a known malarious area of Iran, and to use that definition to evaluate the validity of several epidemic alert thresholds. Epidemic definition variables generated from surveillance data were plotted against weekly malaria counts to assess which most accurately labelled aberrations. Various alert thresholds were then generated from weekly counts or log counts. Finally, the best epidemic definition was used to calculate and compare sensitivities, specificities, detection delays, and areas under ROC curves of the alert thresholds. The best epidemic definition used a minimum duration of four weeks and week-specific and overall smoothed geometric means plus 1.0 standard deviation. It defined 13 epidemics. A modified C-SUM alert of untransformed weekly counts using a threshold of mean+0.25 SD had the highest combined sensitivity and specificity. Untransformed C-SUM alerts also had the highest area under the ROC curve. Defining local malaria epidemics using objective criteria facilitated the evaluation of alert thresholds. This approach needs further study to refine epidemic definitions and prospectively evaluate epidemic alerts.
Prediction of meningococcal meningitis epidemics in western Africa by using climate information
YAKA, D. P.; Sultan, B.; Tarbangdo, F.; Thiaw, W. M.
2013-12-01
(particularly the meridional wind components) and seasonal recrudescence of MCM cases in order to elaborate seasonal occurrence of MCM epidemics prediction models on different spatiotemporal scales. These predictions have been experienced and evaluated by Burkina Meteorological Authority and Health Protection General Direction since 2009. The encouraging results from the monitoring and evaluation of these predictions given by such simple models enable the development of a monitoring and an early warning integrated system of MCM epidemics in Burkina Faso. This experience could be implemented in others African Sahelo-Soudanian countries.
[Paediatric emergencies; example of the management of winter epidemics].
Mercier, Jean-Christophe; Bellettre, Xavier; Lejay, Émilie; Desmarest, Marie; Titomanlio, Luigi
2015-01-01
Every year, epidemics of viral bronchiolitis and gastroenteritis occur with a significant increase in the number of visits (by a factor 1.8) and hospitalisations that can over-exceed bed capacity leading to transfer sick children to other hospitals. This kind of hospital 'crisis' is not limited to paediatrics, big cities or western nations. It is a worldwide worrying problem. Because our hospital sits in the Northern districts of Paris where a large community of m.ncants lives in poverty, our number of visits is high (mean 250 per day), and winter epidemics further jeopardise the difficult equilibrium achieved between quality management and waiting times. Thus, we have taken various initiatives in terms of organisation of the paediatric emergency department and other wards, including a "fast track" clinic, the opening of beds dedicated to winter epidemics, the institution of a "bed manager" in order to more easily find a bed, and a larger use of home hospitalisations. Furthermore, we created a specific committee which may decide on various indicators of tension whether it is necessary to cancel programmed hospitalisations or surgery.in order to resolve the emergency crisis. This kind of organisation can serve as a model for other hospitals facing winter epidemics crises.
REPRODUCTIVE NUMBERS, EPIDEMIC SPREAD AND CONTROL IN A COMMUNITY OF HOUSEHOLDS
Goldstein, E.; Paur, K.; Fraser, C.; Kenah, E.; Wallinga, J.; Lipsitch, M.
2009-01-01
Many of the studies on emerging epidemics (such as SARS and pandemic flu) use mass action models to estimate reproductive numbers and the needed control measures. In reality, transmission patterns are more complex due to the presence of various social networks. One level of complexity can be accommodated by considering a community of households. Our study of transmission dynamics in a community of households emphasizes five types of reproductive numbers for the epidemic spread: household-to-h...
Bursty communication patterns facilitate spreading in a threshold-based epidemic dynamics.
Takaguchi, Taro; Masuda, Naoki; Holme, Petter
2013-01-01
Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity followed by long periods of silence. This burstiness has been shown to affect spreading phenomena; it accelerates epidemic spreading in some cases and slows it down in other cases. We investigate a model of history-dependent contagion. In our model, repeated interactions between susceptible and infected individuals in a short period of time is needed for a susceptible individual to contract infection. We carry out numerical simulations on real temporal network data to find that bursty activity patterns facilitate epidemic spreading in our model.
Bursty communication patterns facilitate spreading in a threshold-based epidemic dynamics.
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Taro Takaguchi
Full Text Available Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity followed by long periods of silence. This burstiness has been shown to affect spreading phenomena; it accelerates epidemic spreading in some cases and slows it down in other cases. We investigate a model of history-dependent contagion. In our model, repeated interactions between susceptible and infected individuals in a short period of time is needed for a susceptible individual to contract infection. We carry out numerical simulations on real temporal network data to find that bursty activity patterns facilitate epidemic spreading in our model.
Defining and detecting malaria epidemics in south-east Iran
Directory of Open Access Journals (Sweden)
McKelvie William R
2012-03-01
Full Text Available Abstract Background A lack of consensus on how to define malaria epidemics has impeded the evaluation of early detection systems. This study aimed to develop local definitions of malaria epidemics in a known malarious area of Iran, and to use that definition to evaluate the validity of several epidemic alert thresholds. Methods Epidemic definition variables generated from surveillance data were plotted against weekly malaria counts to assess which most accurately labelled aberrations. Various alert thresholds were then generated from weekly counts or log counts. Finally, the best epidemic definition was used to calculate and compare sensitivities, specificities, detection delays, and areas under ROC curves of the alert thresholds. Results The best epidemic definition used a minimum duration of four weeks and week-specific and overall smoothed geometric means plus 1.0 standard deviation. It defined 13 epidemics. A modified C-SUM alert of untransformed weekly counts using a threshold of mean + 0.25 SD had the highest combined sensitivity and specificity. Untransformed C-SUM alerts also had the highest area under the ROC curve. Conclusions Defining local malaria epidemics using objective criteria facilitated the evaluation of alert thresholds. This approach needs further study to refine epidemic definitions and prospectively evaluate epidemic alerts.
International Nuclear Information System (INIS)
Wu, An-Cai
2014-01-01
Recent empirical analyses of some realistic dynamical networks have demonstrated that their degree distributions are stable scale-free (SF), but the instantaneous well-connected hubs at one point of time can quickly become weakly connected. Motivated by these empirical results, we propose a simple toy dynamical agent-to-agent contact network model, in which each agent stays at one node of a static underlay network and the nearest neighbors swap their positions with each other. Although the degree distribution of the dynamical network model at any one time is equal to that in the static underlay network, the numbers and identities of each agent’s contacts will change over time. It is found that the dynamic interaction tends to suppress epidemic spreading in terms of larger epidemic threshold, smaller prevalence (the fraction of infected individuals) and smaller velocity of epidemic outbreak. Furthermore, the dynamic interaction results in the prevalence to undergo a phase transition at a finite threshold of the epidemic spread rate in the thermodynamic limit, which is in contradiction to the absence of an epidemic threshold in static SF networks. Some of these findings obtained from heterogeneous mean-field theory are in good agreement with numerical simulations. (paper)
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Daniela Bezemer
2015-11-01
Full Text Available The HIV-1 subtype B epidemic amongst men who have sex with men (MSM is resurgent in many countries despite the widespread use of effective combination antiretroviral therapy (cART. In this combined mathematical and phylogenetic study of observational data, we aimed to find out the extent to which the resurgent epidemic is the result of newly introduced strains or of growth of already circulating strains.As of November 2011, the ATHENA observational HIV cohort of all patients in care in the Netherlands since 1996 included HIV-1 subtype B polymerase sequences from 5,852 patients. Patients who were diagnosed between 1981 and 1995 were included in the cohort if they were still alive in 1996. The ten most similar sequences to each ATHENA sequence were selected from the Los Alamos HIV Sequence Database, and a phylogenetic tree was created of a total of 8,320 sequences. Large transmission clusters that included ≥10 ATHENA sequences were selected, with a local support value ≥ 0.9 and median pairwise patristic distance below the fifth percentile of distances in the whole tree. Time-varying reproduction numbers of the large MSM-majority clusters were estimated through mathematical modeling. We identified 106 large transmission clusters, including 3,061 (52% ATHENA and 652 Los Alamos sequences. Half of the HIV sequences from MSM registered in the cohort in the Netherlands (2,128 of 4,288 were included in 91 large MSM-majority clusters. Strikingly, at least 54 (59% of these 91 MSM-majority clusters were already circulating before 1996, when cART was introduced, and have persisted to the present. Overall, 1,226 (35% of the 3,460 diagnoses among MSM since 1996 were found in these 54 long-standing clusters. The reproduction numbers of all large MSM-majority clusters were around the epidemic threshold value of one over the whole study period. A tendency towards higher numbers was visible in recent years, especially in the more recently introduced clusters
Diffusive epidemic process: theory and simulation
International Nuclear Information System (INIS)
Maia, Daniel Souza; Dickman, Ronald
2007-01-01
We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo reactions B → A and A+B → 2B; the total particle number is conserved. We formulate the model as a continuous-time Markov process described by a master equation. A phase transition between the (absorbing) B-free state and an active state is observed as the parameters (reaction and diffusion rates, and total particle density) are varied. Mean-field theory reveals a surprising, nonmonotonic dependence of the critical recovery rate on the diffusion rate of B particles. A computational realization of the process that is faithful to the transition rates defining the model is devised, allowing for direct comparison with theory. Using the quasi-stationary simulation method we determine the order parameter and the survival time in systems of up to 4000 sites. Due to strong finite-size effects, the results converge only for large system sizes. We find no evidence for a discontinuous transition. Our results are consistent with the existence of three distinct universality classes, depending on whether A particles diffusive more rapidly, less rapidly or at the same rate as B particles. We also perform quasi-stationary simulations of the triplet creation model, which yield results consistent with a discontinuous transition at high diffusion rates
Unsynchronized influenza epidemics in two neighboring subtropical cities
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Xiujuan Tang
2018-04-01
Full Text Available Objective: The aim of this study was to examine the synchrony of influenza epidemics between Hong Kong and Shenzhen, two neighboring subtropical cities in South China. Methods: Laboratory-confirmed influenza data for the period January 2006 to December 2016 were obtained from the Shenzhen Center for Disease Control and Prevention and the Department of Health in Hong Kong. The population data were retrieved from the 2011 population censuses. The weekly rates of laboratory-confirmed influenza cases were compared between Shenzhen and Hong Kong. Results: Unsynchronized influenza epidemics between Hong Kong and Shenzhen were frequently observed during the study period. Influenza A/H1N1 caused a more severe pandemic in Hong Kong in 2009, but the subsequent seasonal epidemics showed similar magnitudes in both cities. Two influenza A/H3N2 dominant epidemic waves were seen in Hong Kong in 2015, but these epidemics were very minor in Shenzhen. More influenza B epidemics occurred in Shenzhen than in Hong Kong. Conclusions: Influenza epidemics appeared to be unsynchronized between Hong Kong and Shenzhen most of the time. Given the close geographical locations of these two cities, this could be due to the strikingly different age structures of their populations. Keywords: Influenza epidemics, Synchrony, Shenzhen, Hong Kong
Impact of human mobility on the emergence of dengue epidemics in Pakistan
Wesolowski, Amy; Qureshi, Taimur; Boni, Maciej F.; Sundsøy, Pål Roe; Johansson, Michael A.; Rasheed, Syed Basit; Engø-Monsen, Kenth; Buckee, Caroline O.
2015-01-01
The recent emergence of dengue viruses into new susceptible human populations throughout Asia and the Middle East, driven in part by human travel on both local and global scales, represents a significant global health risk, particularly in areas with changing climatic suitability for the mosquito vector. In Pakistan, dengue has been endemic for decades in the southern port city of Karachi, but large epidemics in the northeast have emerged only since 2011. Pakistan is therefore representative of many countries on the verge of countrywide endemic dengue transmission, where prevention, surveillance, and preparedness are key priorities in previously dengue-free regions. We analyze spatially explicit dengue case data from a large outbreak in Pakistan in 2013 and compare the dynamics of the epidemic to an epidemiological model of dengue virus transmission based on climate and mobility data from ∼40 million mobile phone subscribers. We find that mobile phone-based mobility estimates predict the geographic spread and timing of epidemics in both recently epidemic and emerging locations. We combine transmission suitability maps with estimates of seasonal dengue virus importation to generate fine-scale dynamic risk maps with direct application to dengue containment and epidemic preparedness. PMID:26351662
Food system consequences of a fungal disease epidemic in a major crop.
Godfray, H Charles J; Mason-D'Croz, Daniel; Robinson, Sherman
2016-12-05
Fungal diseases are major threats to the most important crops upon which humanity depends. Were there to be a major epidemic that severely reduced yields, its effects would spread throughout the globalized food system. To explore these ramifications, we use a partial equilibrium economic model of the global food system (IMPACT) to study a hypothetical severe but short-lived epidemic that reduces rice yields in the countries affected by 80%. We modelled a succession of epidemic scenarios of increasing severity, starting with the disease in a single country in southeast Asia and ending with the pathogen present in most of eastern Asia. The epidemic and subsequent crop losses led to substantially increased global rice prices. However, as long as global commodity trade was unrestricted and able to respond fast enough, the effects on individual calorie consumption were, to a large part, mitigated. Some of the worse effects were projected to be experienced by poor net-rice importing countries in sub-Saharan Africa, which were not affected directly by the disease but suffered because of higher rice prices. We critique the assumptions of our models and explore political economic pressures to restrict trade at times of crisis. We finish by arguing for the importance of 'stress-testing' the resilience of the global food system to crop disease and other shocks.This article is part of the themed issue 'Tackling emerging fungal threats to animal health, food security and ecosystem resilience'. © 2016 The Author(s).
Phylodynamic analysis of HIV sub-epidemics in Mochudi, Botswana
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Vlad Novitsky
2015-12-01
Real-time HIV genotyping and breaking down local HIV epidemics into phylogenetically distinct sub-epidemics may help to reveal the structure and dynamics of HIV transmission networks in communities, and aid in the design of targeted interventions for members of the acute sub-epidemics that likely fuel local HIV/AIDS epidemics.
Characterizing the reproduction number of epidemics with early subexponential growth dynamics.
Chowell, Gerardo; Viboud, Cécile; Simonsen, Lone; Moghadas, Seyed M
2016-10-01
Early estimates of the transmission potential of emerging and re-emerging infections are increasingly used to inform public health authorities on the level of risk posed by outbreaks. Existing methods to estimate the reproduction number generally assume exponential growth in case incidence in the first few disease generations, before susceptible depletion sets in. In reality, outbreaks can display subexponential (i.e. polynomial) growth in the first few disease generations, owing to clustering in contact patterns, spatial effects, inhomogeneous mixing, reactive behaviour changes or other mechanisms. Here, we introduce the generalized growth model to characterize the early growth profile of outbreaks and estimate the effective reproduction number, with no need for explicit assumptions about the shape of epidemic growth. We demonstrate this phenomenological approach using analytical results and simulations from mechanistic models, and provide validation against a range of empirical disease datasets. Our results suggest that subexponential growth in the early phase of an epidemic is the rule rather the exception. Mechanistic simulations show that slight modifications to the classical susceptible-infectious-removed model result in subexponential growth, and in turn a rapid decline in the reproduction number within three to five disease generations. For empirical outbreaks, the generalized-growth model consistently outperforms the exponential model for a variety of directly and indirectly transmitted diseases datasets (pandemic influenza, measles, smallpox, bubonic plague, cholera, foot-and-mouth disease, HIV/AIDS and Ebola) with model estimates supporting subexponential growth dynamics. The rapid decline in effective reproduction number predicted by analytical results and observed in real and synthetic datasets within three to five disease generations contrasts with the expectation of invariant reproduction number in epidemics obeying exponential growth. The
Characterizing the reproduction number of epidemics with early subexponential growth dynamics
Viboud, Cécile; Simonsen, Lone; Moghadas, Seyed M.
2016-01-01
Early estimates of the transmission potential of emerging and re-emerging infections are increasingly used to inform public health authorities on the level of risk posed by outbreaks. Existing methods to estimate the reproduction number generally assume exponential growth in case incidence in the first few disease generations, before susceptible depletion sets in. In reality, outbreaks can display subexponential (i.e. polynomial) growth in the first few disease generations, owing to clustering in contact patterns, spatial effects, inhomogeneous mixing, reactive behaviour changes or other mechanisms. Here, we introduce the generalized growth model to characterize the early growth profile of outbreaks and estimate the effective reproduction number, with no need for explicit assumptions about the shape of epidemic growth. We demonstrate this phenomenological approach using analytical results and simulations from mechanistic models, and provide validation against a range of empirical disease datasets. Our results suggest that subexponential growth in the early phase of an epidemic is the rule rather the exception. Mechanistic simulations show that slight modifications to the classical susceptible–infectious–removed model result in subexponential growth, and in turn a rapid decline in the reproduction number within three to five disease generations. For empirical outbreaks, the generalized-growth model consistently outperforms the exponential model for a variety of directly and indirectly transmitted diseases datasets (pandemic influenza, measles, smallpox, bubonic plague, cholera, foot-and-mouth disease, HIV/AIDS and Ebola) with model estimates supporting subexponential growth dynamics. The rapid decline in effective reproduction number predicted by analytical results and observed in real and synthetic datasets within three to five disease generations contrasts with the expectation of invariant reproduction number in epidemics obeying exponential growth. The
A threshold limit theorem for the stochastic logistic epidemic
Andersson, Håkan; Djehiche, Boualem
1998-01-01
The time until extinction for the closed SIS stochastic logistic epidemic model is investigated. We derive the asymptotic distribution for the extinction time as the population grows to infinity, under different initial conditions and for different values of the infection rate.
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Wang Wei
Full Text Available This study was aimed to find out epidemiologic characteristic of tuberculosis (TB cases, and Human Immunodeficiency Virus (HIV positive cases among TB patients (TB/HIV co-infection through demographic, temporal, and spatial study in Urumqi.Descriptive statistics and multivariate logistic regression were applied to identify the epidemiologic characteristics and risk factors of TB epidemic and TB/HIV co-infection epidemic. All addresses of each TB case, TB/HIV co-infection case, and administrative street were transformed into geographical coordinate. Subsequently, the geocoded address for 82 streets was transformed into a dot map used as the basis of spatial datasets. In addition, the paper also used quantile map and the spatial scan statistic in order to identify the spatial distribution and spatial clusters of TB epidemic and TB/HIV co-infection epidemic.There was a declining trend of the notification rates of TB epidemic from 2007 to 2009, as well as a rising trend from 2010 to 2013. However, the notification rates of TB/HIV co-infection epidemic showed a rising trend from 2007 to 2010, and a declining trend from 2011 to 2013. Moreover, a significant share of TB epidemic and TB/HIV co-infection epidemic happened between the age of 15 to 45 years old, indicating an increase in risk of TB and TB/HIV infection. It is worth noting that the risk of HIV infection for male TB patients was 2.947 times (95% CI [2.178, 3.988] than that of female patients. Han ethnicity and Uygur ethnicity in urban region accounted for a large proportion of total TB and TB/HIV co-infection cases. Most of the TB cases of minorities in Urumqi showed a statistically significant increase in risk of HIV infection than Han ethnicity in Urumqi. In addition, the spatial distribution of TB epidemic and TB/HIV co-infection epidemic was highly skewed. Most of the local clusters were located in urban area and rural-urban continuum where showed an increase in risk of TB and TB
Immunization strategy for epidemic spreading on multilayer networks
Buono, C.; Braunstein, L. A.
2015-01-01
In many real-world complex systems, individuals have many kinds of interactions among them, suggesting that it is necessary to consider a layered-structure framework to model systems such as social interactions. This structure can be captured by multilayer networks and can have major effects on the spreading of process that occurs over them, such as epidemics. In this letter we study a targeted immunization strategy for epidemic spreading over a multilayer network. We apply the strategy in one of the layers and study its effect in all layers of the network disregarding degree-degree correlation among layers. We found that the targeted strategy is not as efficient as in isolated networks, due to the fact that in order to stop the spreading of the disease it is necessary to immunize more than 80% of the individuals. However, the size of the epidemic is drastically reduced in the layer where the immunization strategy is applied compared to the case with no mitigation strategy. Thus, the immunization strategy has a major effect on the layer were it is applied, but does not efficiently protect the individuals of other layers.
First dengue haemorrhagic fever epidemic in the Americas, 1981: insights into the causative agent.
Rodriguez-Roche, Rosmari; Hinojosa, Yoandri; Guzman, Maria G
2014-12-01
Historical records describe a disease in North America that clinically resembled dengue haemorrhagic fever during the latter part of the slave-trading period. However, the dengue epidemic that occurred in Cuba in 1981 was the first laboratory-confirmed and clinically diagnosed outbreak of dengue haemorrhagic fever in the Americas. At that time, the presumed source of the dengue type 2 strain isolated during this epidemic was considered controversial, partly because of the limited sequence data and partly because the origin of the virus appeared to be southern Asia. Here, we present a molecular characterisation at the whole-genome level of the original strains isolated at different time points during the epidemic. Phylogenetic trees constructed using Bayesian methods indicated that 1981 Cuban strains group within the Asian 2 genotype. In addition, the study revealed that viral evolution occurred during the epidemic - a fact that could be related to the increasing severity from month to month. Moreover, the Cuban strains exhibited particular amino acid substitutions that differentiate them from the New Guinea C prototype strain as well as from dengue type 2 strains isolated globally.
Malaria epidemic and drug resistance, Djibouti.
Rogier, Christophe; Pradines, Bruno; Bogreau, H; Koeck, Jean-Louis; Kamil, Mohamed-Ali; Mercereau-Puijalon, Odile
2005-02-01
Analysis of Plasmodium falciparum isolates collected before, during, and after a 1999 malaria epidemic in Djibouti shows that, despite a high prevalence of resistance to chloroquine, the epidemic cannot be attributed to a sudden increase in drug resistance of local parasite populations.
Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function
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Jinhong Zhang
2014-01-01
Full Text Available The dynamics of SEIR epidemic model with saturated incidence rate and saturated treatment function are explored in this paper. The basic reproduction number that determines disease extinction and disease survival is given. The existing threshold conditions of all kinds of the equilibrium points are obtained. Sufficient conditions are established for the existence of backward bifurcation. The local asymptotical stability of equilibrium is verified by analyzing the eigenvalues and using the Routh-Hurwitz criterion. We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease. Numerical simulations are presented to support and complement the theoretical findings.
A standard protocol for describing individual-based and agent-based models
Grimm, Volker; Berger, Uta; Bastiansen, Finn; Eliassen, Sigrunn; Ginot, Vincent; Giske, Jarl; Goss-Custard, John; Grand, Tamara; Heinz, Simone K.; Huse, Geir; Huth, Andreas; Jepsen, Jane U.; Jorgensen, Christian; Mooij, Wolf M.; Muller, Birgit; Pe'er, Guy; Piou, Cyril; Railsback, Steven F.; Robbins, Andrew M.; Robbins, Martha M.; Rossmanith, Eva; Ruger, Nadja; Strand, Espen; Souissi, Sami; Stillman, Richard A.; Vabo, Rune; Visser, Ute; DeAngelis, Donald L.
2006-01-01
Simulation models that describe autonomous individual organisms (individual based models, IBM) or agents (agent-based models, ABM) have become a widely used tool, not only in ecology, but also in many other disciplines dealing with complex systems made up of autonomous entities. However, there is no standard protocol for describing such simulation models, which can make them difficult to understand and to duplicate. This paper presents a proposed standard protocol, ODD, for describing IBMs and ABMs, developed and tested by 28 modellers who cover a wide range of fields within ecology. This protocol consists of three blocks (Overview, Design concepts, and Details), which are subdivided into seven elements: Purpose, State variables and scales, Process overview and scheduling, Design concepts, Initialization, Input, and Submodels. We explain which aspects of a model should be described in each element, and we present an example to illustrate the protocol in use. In addition, 19 examples are available in an Online Appendix. We consider ODD as a first step for establishing a more detailed common format of the description of IBMs and ABMs. Once initiated, the protocol will hopefully evolve as it becomes used by a sufficiently large proportion of modellers.
Network Performance Improvement under Epidemic Failures in Optical Transport Networks
DEFF Research Database (Denmark)
Fagertun, Anna Manolova; Ruepp, Sarah Renée
2013-01-01
In this paper we investigate epidemic failure spreading in large- scale GMPLS-controlled transport networks. By evaluating the effect of the epidemic failure spreading on the network, we design several strategies for cost-effective network performance improvement via differentiated repair times....... First we identify the most vulnerable and the most strategic nodes in the network. Then, via extensive simulations we show that strategic placement of resources for improved failure recovery has better performance than randomly assigning lower repair times among the network nodes. Our OPNET simulation...... model can be used during the network planning process for facilitating cost- effective network survivability design....
Rasmita Panigrahi; Trilochan Rout
2012-01-01
Classifying nodes in a network is a task with wide range of applications .it can be particularly useful in epidemics detection .Many resources are invested in the task of epidemics and precisely allow human investigators to work more efficiently. This work creates random and scale- free graphs the simulations with varying relative infectiousness and graph size performed. By using computer simulations it should be possible to model such epidemic Phenomena and to better understand the role play...
Homo-psychologicus: Reactionary behavioural aspects of epidemics
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Alhaji Cherif
2016-03-01
Full Text Available We formulate an in silico model of pathogen avoidance mechanism and investigate its impact on defensive behavioural measures (e.g., spontaneous social exclusions and distancing, crowd avoidance and voluntary vaccination adaptation. In particular, we use SIR(BS (e.g., susceptible-infected-recovered with additional behavioural component model to investigate the impact of homo-psychologicus aspects of epidemics. We focus on reactionary behavioural changes, which apply to both social distancing and voluntary vaccination participations. Our analyses reveal complex relationships between spontaneous and uncoordinated behavioural changes, the emergence of its contagion properties, and mitigation of infectious diseases. We find that the presence of effective behavioural changes can impede the persistence of disease. Furthermore, it was found that under perfect effective behavioural change, there are three regions in the response factor (e.g., imitation and/or reactionary and behavioural scale factor (e.g., global/local factors ρ–α behavioural space. Mainly, (1 disease is always endemic even in the presence of behavioural change, (2 behavioural-prevalence plasticity is observed and disease can sometimes be eradication, and (3 elimination of endemic disease under permanence of permanent behavioural change is achieved. These results suggest that preventive behavioural changes (e.g., non-pharmaceutical prophylactic measures, social distancing and exclusion, crowd avoidance are influenced by individual differences in perception of risks and are a salient feature of epidemics. Additionally, these findings indicates that care needs to be taken when considering the effect of adaptive behavioural change in predicting the course of epidemics, and as well as the interpretation and development of the public health measures that account for spontaneous behavioural changes.
Homo-psychologicus: Reactionary behavioural aspects of epidemics.
Cherif, Alhaji; Barley, Kamal; Hurtado, Marcel
2016-03-01
We formulate an in silico model of pathogen avoidance mechanism and investigate its impact on defensive behavioural measures (e.g., spontaneous social exclusions and distancing, crowd avoidance and voluntary vaccination adaptation). In particular, we use SIR(B)S (e.g., susceptible-infected-recovered with additional behavioural component) model to investigate the impact of homo-psychologicus aspects of epidemics. We focus on reactionary behavioural changes, which apply to both social distancing and voluntary vaccination participations. Our analyses reveal complex relationships between spontaneous and uncoordinated behavioural changes, the emergence of its contagion properties, and mitigation of infectious diseases. We find that the presence of effective behavioural changes can impede the persistence of disease. Furthermore, it was found that under perfect effective behavioural change, there are three regions in the response factor (e.g., imitation and/or reactionary) and behavioural scale factor (e.g., global/local) factors ρ-α behavioural space. Mainly, (1) disease is always endemic even in the presence of behavioural change, (2) behavioural-prevalence plasticity is observed and disease can sometimes be eradication, and (3) elimination of endemic disease under permanence of permanent behavioural change is achieved. These results suggest that preventive behavioural changes (e.g., non-pharmaceutical prophylactic measures, social distancing and exclusion, crowd avoidance) are influenced by individual differences in perception of risks and are a salient feature of epidemics. Additionally, these findings indicates that care needs to be taken when considering the effect of adaptive behavioural change in predicting the course of epidemics, and as well as the interpretation and development of the public health measures that account for spontaneous behavioural changes. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.
Planning horizon affects prophylactic decision-making and epidemic dynamics.
Nardin, Luis G; Miller, Craig R; Ridenhour, Benjamin J; Krone, Stephen M; Joyce, Paul; Baumgaertner, Bert O
2016-01-01
The spread of infectious diseases can be impacted by human behavior, and behavioral decisions often depend implicitly on a planning horizon-the time in the future over which options are weighed. We investigate the effects of planning horizons on epidemic dynamics. We developed an epidemiological agent-based model (along with an ODE analog) to explore the decision-making of self-interested individuals on adopting prophylactic behavior. The decision-making process incorporates prophylaxis efficacy and disease prevalence with the individuals' payoffs and planning horizon. Our results show that for short and long planning horizons individuals do not consider engaging in prophylactic behavior. In contrast, individuals adopt prophylactic behavior when considering intermediate planning horizons. Such adoption, however, is not always monotonically associated with the prevalence of the disease, depending on the perceived protection efficacy and the disease parameters. Adoption of prophylactic behavior reduces the epidemic peak size while prolonging the epidemic and potentially generates secondary waves of infection. These effects can be made stronger by increasing the behavioral decision frequency or distorting an individual's perceived risk of infection.
Epidemic mitigation via awareness propagation in communication networks: the role of time scales
Wang, Huijuan; Chen, Chuyi; Qu, Bo; Li, Daqing; Havlin, Shlomo
2017-07-01
The participation of individuals in multi-layer networks allows for feedback between network layers, opening new possibilities to mitigate epidemic spreading. For instance, the spread of a biological disease such as Ebola in a physical contact network may trigger the propagation of the information related to this disease in a communication network, e.g. an online social network. The information propagated in the communication network may increase the awareness of some individuals, resulting in them avoiding contact with their infected neighbors in the physical contact network, which might protect the population from the infection. In this work, we aim to understand how the time scale γ of the information propagation (speed that information is spread and forgotten) in the communication network relative to that of the epidemic spread (speed that an epidemic is spread and cured) in the physical contact network influences such mitigation using awareness information. We begin by proposing a model of the interaction between information propagation and epidemic spread, taking into account the relative time scale γ. We analytically derive the average fraction of infected nodes in the meta-stable state for this model (i) by developing an individual-based mean-field approximation (IBMFA) method and (ii) by extending the microscopic Markov chain approach (MMCA). We show that when the time scale γ of the information spread relative to the epidemic spread is large, our IBMFA approximation is better compared to MMCA near the epidemic threshold, whereas MMCA performs better when the prevalence of the epidemic is high. Furthermore, we find that an optimal mitigation exists that leads to a minimal fraction of infected nodes. The optimal mitigation is achieved at a non-trivial relative time scale γ, which depends on the rate at which an infected individual becomes aware. Contrary to our intuition, information spread too fast in the communication network could reduce the
Carnegie, Nicole Bohme
2018-01-30
Understanding the dynamics of disease spread is key to developing effective interventions to control or prevent an epidemic. The structure of the network of contacts over which the disease spreads has been shown to have a strong influence on the outcome of the epidemic, but an open question remains as to whether it is possible to estimate contact network features from data collected in an epidemic. The approach taken in this paper is to examine the distributions of epidemic outcomes arising from epidemics on networks with particular structural features to assess whether that structure could be measured from epidemic data and what other constraints might be needed to make the problem identifiable. To this end, we vary the network size, mean degree, and transmissibility of the pathogen, as well as the network feature of interest: clustering, degree assortativity, or attribute-based preferential mixing. We record several standard measures of the size and spread of the epidemic, as well as measures that describe the shape of the transmission tree in order to ascertain whether there are detectable signals in the final data from the outbreak. The results suggest that there is potential to estimate contact network features from transmission trees or pure epidemic data, particularly for diseases with high transmissibility or for which the relevant contact network is of low mean degree. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.
Can epidemics be non-communicable?
DEFF Research Database (Denmark)
Seeberg, Jens; Meinert, Lotte
2015-01-01
This article argues that the concept of communicability that is central to the distinction between communicable diseases (CDs) and noncommunicable diseases (NCDs) is poorly conceptualized. The epidemic spread of NCDs such as diabetes, depression, and eating disorders demonstrates...... that they are communicable, even if they are not infectious. We need to more critically explore how they might be communicable in specific environments. All diseases with epidemic potential, we argue, should be assumed to be commun icable in a broader sense, and that the underlying medical distinction between infectious...... and noninfectious diseases confuses our understanding of NCD epidemics when these categories are treated as synonymous with ‘communicable’ and ‘noncommunicable’ diseases, respectively. The dominant role accorded to the concept of ‘lifestyle’, with its focus on individual responsibility, is part of the problem...
Coupling effects on turning points of infectious diseases epidemics in scale-free networks.
Kim, Kiseong; Lee, Sangyeon; Lee, Doheon; Lee, Kwang Hyung
2017-05-31
Pandemic is a typical spreading phenomenon that can be observed in the human society and is dependent on the structure of the social network. The Susceptible-Infective-Recovered (SIR) model describes spreading phenomena using two spreading factors; contagiousness (β) and recovery rate (γ). Some network models are trying to reflect the social network, but the real structure is difficult to uncover. We have developed a spreading phenomenon simulator that can input the epidemic parameters and network parameters and performed the experiment of disease propagation. The simulation result was analyzed to construct a new marker VRTP distribution. We also induced the VRTP formula for three of the network mathematical models. We suggest new marker VRTP (value of recovered on turning point) to describe the coupling between the SIR spreading and the Scale-free (SF) network and observe the aspects of the coupling effects with the various of spreading and network parameters. We also derive the analytic formulation of VRTP in the fully mixed model, the configuration model, and the degree-based model respectively in the mathematical function form for the insights on the relationship between experimental simulation and theoretical consideration. We discover the coupling effect between SIR spreading and SF network through devising novel marker VRTP which reflects the shifting effect and relates to entropy.
Grefenstette, John J; Brown, Shawn T; Rosenfeld, Roni; DePasse, Jay; Stone, Nathan T B; Cooley, Phillip C; Wheaton, William D; Fyshe, Alona; Galloway, David D; Sriram, Anuroop; Guclu, Hasan; Abraham, Thomas; Burke, Donald S
2013-10-08
Mathematical and computational models provide valuable tools that help public health planners to evaluate competing health interventions, especially for novel circumstances that cannot be examined through observational or controlled studies, such as pandemic influenza. The spread of diseases like influenza depends on the mixing patterns within the population, and these mixing patterns depend in part on local factors including the spatial distribution and age structure of the population, the distribution of size and composition of households, employment status and commuting patterns of adults, and the size and age structure of schools. Finally, public health planners must take into account the health behavior patterns of the population, patterns that often vary according to socioeconomic factors such as race, household income, and education levels. FRED (a Framework for Reconstructing Epidemic Dynamics) is a freely available open-source agent-based modeling system based closely on models used in previously published studies of pandemic influenza. This version of FRED uses open-access census-based synthetic populations that capture the demographic and geographic heterogeneities of the population, including realistic household, school, and workplace social networks. FRED epidemic models are currently available for every state and county in the United States, and for selected international locations. State and county public health planners can use FRED to explore the effects of possible influenza epidemics in specific geographic regions of interest and to help evaluate the effect of interventions such as vaccination programs and school closure policies. FRED is available under a free open source license in order to contribute to the development of better modeling tools and to encourage open discussion of modeling tools being used to evaluate public health policies. We also welcome participation by other researchers in the further development of FRED.
HERMES: A Model to Describe Deformation, Burning, Explosion, and Detonation
Energy Technology Data Exchange (ETDEWEB)
Reaugh, J E
2011-11-22
HERMES (High Explosive Response to MEchanical Stimulus) was developed to fill the need for a model to describe an explosive response of the type described as BVR (Burn to Violent Response) or HEVR (High Explosive Violent Response). Characteristically this response leaves a substantial amount of explosive unconsumed, the time to reaction is long, and the peak pressure developed is low. In contrast, detonations characteristically consume all explosive present, the time to reaction is short, and peak pressures are high. However, most of the previous models to describe explosive response were models for detonation. The earliest models to describe the response of explosives to mechanical stimulus in computer simulations were applied to intentional detonation (performance) of nearly ideal explosives. In this case, an ideal explosive is one with a vanishingly small reaction zone. A detonation is supersonic with respect to the undetonated explosive (reactant). The reactant cannot respond to the pressure of the detonation before the detonation front arrives, so the precise compressibility of the reactant does not matter. Further, the mesh sizes that were practical for the computer resources then available were large with respect to the reaction zone. As a result, methods then used to model detonations, known as {beta}-burn or program burn, were not intended to resolve the structure of the reaction zone. Instead, these methods spread the detonation front over a few finite-difference zones, in the same spirit that artificial viscosity is used to spread the shock front in inert materials over a few finite-difference zones. These methods are still widely used when the structure of the reaction zone and the build-up to detonation are unimportant. Later detonation models resolved the reaction zone. These models were applied both to performance, particularly as it is affected by the size of the charge, and to situations in which the stimulus was less than that needed for reliable
Ten Putative Contributors to the Obesity Epidemic
McAllister, Emily J.; Dhurandhar, Nikhil V.; Keith, Scott W.; Aronne, Louis J.; Barger, Jamie; Baskin, Monica; Benca, Ruth M.; Biggio, Joseph; Boggiano, Mary M.; Eisenmann, Joe C.; Elobeid, Mai; Fontaine, Kevin R.; Gluckman, Peter; Hanlon, Erin C.; Katzmarzyk, Peter; Pietrobelli, Angelo; Redden, David T.; Ruden, Douglas M.; Wang, Chenxi; Waterland, Robert A.; Wright, Suzanne M.; Allison, David B.
2010-01-01
The obesity epidemic is a global issue and shows no signs of abating, while the cause of this epidemic remains unclear. Marketing practices of energy-dense foods and institutionally-driven declines in physical activity are the alleged perpetrators for the epidemic, despite a lack of solid evidence to demonstrate their causal role. While both may contribute to obesity, we call attention to their unquestioned dominance in program funding and public efforts to reduce obesity, and propose several alternative putative contributors that would benefit from equal consideration and attention. Evidence for microorganisms, epigenetics, increasing maternal age, greater fecundity among people with higher adiposity, assortative mating, sleep debt, endocrine disruptors, pharmaceutical iatrogenesis, reduction in variability of ambient temperatures, and intrauterine and intergenerational effects, as contributing factors to the obesity epidemic are reviewed herein. While the evidence is strong for some contributors such as pharmaceutical-induced weight gain, it is still emerging for other reviewed factors. Considering the role of such putative etiological factors of obesity may lead to comprehensive, cause specific, and effective strategies for prevention and treatment of this global epidemic. PMID:19960394
Jiao, Jianjun; Cai, Shaohong; Li, Limei
2016-05-01
To understand the effect of impulsive vaccination and restricting infected individuals boarding transports on disease spread, we establish an SIR model with impulsive vaccination, impulsive dispersal and restricting infected individuals boarding transports. This SIR epidemic model for two regions, which are connected by transportation of non-infected individuals, portrays the evolvement of diseases. We prove that all solutions of the investigated system are uniformly ultimately bounded. We also prove that there exists globally asymptotically stable infection-free boundary periodic solution. The condition for permanence is discussed. It is concluded that the approach of impulsive vaccination and restricting infected individuals boarding transports provides reliable tactic basis for preventing disease spread.
Modeling the spread of vector-borne diseases on bipartite networks.
Directory of Open Access Journals (Sweden)
Donal Bisanzio
Full Text Available BACKGROUND: Vector-borne diseases for which transmission occurs exclusively between vectors and hosts can be modeled as spreading on a bipartite network. METHODOLOGY/PRINCIPAL FINDINGS: In such models the spreading of the disease strongly depends on the degree distribution of the two classes of nodes. It is sufficient for one of the classes to have a scale-free degree distribution with a slow enough decay for the network to have asymptotically vanishing epidemic threshold. Data on the distribution of Ixodes ricinus ticks on mice and lizards from two independent studies are well described by a scale-free distribution compatible with an asymptotically vanishing epidemic threshold. The commonly used negative binomial, instead, cannot describe the right tail of the empirical distribution. CONCLUSIONS/SIGNIFICANCE: The extreme aggregation of vectors on hosts, described by the power-law decay of the degree distribution, makes the epidemic threshold decrease with the size of the network and vanish asymptotically.
Lemos, Daniele Rocha Queiroz; Franco, Aidée Ramirez; de Sá Roriz, Maria Lúcia Feitosa; Carneiro, Ana Karine Borges; de Oliveira Garcia, Márcio Henrique; de Souza, Fábia Lidiana; Duron Andino, Regina; de Góes Cavalcanti, Luciano Pamplona
2017-03-23
The measles virus circulation was halted in Brazil in 2001 and the country has a routine vaccination coverage against measles, mumps and rubella higher than 95%. In Ceará, the last confirmed case was in 1999. This article describes the strategies adopted and the effectiveness of surveillance and control measures implemented during a measles epidemic in the post-elimination period. The epidemic started in December 2013 and lasted 20 months, reaching 38 cities and 1,052 confirmed cases. The D8 genotype was identified. More than 50,000 samples were tested for measles and 86.4% of the confirmed cases had a laboratory diagnosis. The beginning of an campaign vaccination was delayed in part by the availability of vaccine. The classic control measures were not enough to control the epidemic. The creation of a committee of experts, the agreement signed between managers of the three spheres of government, the conducting of an institutional active search of suspected cases, vaccination door to door at alternative times, the use of micro planning, a broad advertising campaign at local media and technical operative support contributed to containing the epidemic. It is important to recognize the possibility of epidemics at this stage of post-elimination and prepare a sensitive surveillance system for timely response. Copyright © 2017 Elsevier Ltd. All rights reserved.
Statistics of Epidemics in Networks by Passing Messages
Shrestha, Munik Kumar
Epidemic processes are common out-of-equilibrium phenomena of broad interdisciplinary interest. In this thesis, we show how message-passing approach can be a helpful tool for simulating epidemic models in disordered medium like networks, and in particular for estimating the probability that a given node will become infectious at a particular time. The sort of dynamics we consider are stochastic, where randomness can arise from the stochastic events or from the randomness of network structures. As in belief propagation, variables or messages in message-passing approach are defined on the directed edges of a network. However, unlike belief propagation, where the posterior distributions are updated according to Bayes' rule, in message-passing approach we write differential equations for the messages over time. It takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source, and thus avoids "echo chamber effects" where a pair of adjacent nodes each amplify the probability that the other is infectious. In our first results, we develop a message-passing approach to threshold models of behavior popular in sociology. These are models, first proposed by Granovetter, where individuals have to hear about a trend or behavior from some number of neighbors before adopting it themselves. In thermodynamic limit of large random networks, we provide an exact analytic scheme while calculating the time dependence of the probabilities and thus learning about the whole dynamics of bootstrap percolation, which is a simple model known in statistical physics for exhibiting discontinuous phase transition. As an application, we apply a similar model to financial networks, studying when bankruptcies spread due to the sudden devaluation of shared assets in overlapping portfolios. We predict that although diversification may be good for individual institutions, it can create dangerous systemic effects, and as a result
Control of African swine fever epidemics in industrialized swine populations
DEFF Research Database (Denmark)
Hisham Beshara Halasa, Tariq; Bøtner, Anette; Mortensen, Sten
2016-01-01
, it is important to explore strategies that can effectively control an epidemic of ASF. In this study, the epidemiological and economic effects of strategies to control the spread of ASF between domestic swine herds were examined using a published model (DTU-DADS-ASF). The control strategies were the basic EU...... and national strategy (Basic), the basic strategy plus pre-emptive depopulation of neighboring swine herds, and intensive surveillance of herds in the control zones, including testing live or dead animals. Virus spread via wild boar was not modelled. Under the basic control strategy, the median epidemic......African swine fever (ASF) is a notifiable infectious disease with a high impact on swine health. The disease is endemic in certain regions in the Baltic countries and has spread to Poland constituting a risk of ASF spread toward Western Europe. Therefore, as part of contingency planning...
Threshold dynamics and ergodicity of an SIRS epidemic model with Markovian switching
Li, Dan; Liu, Shengqiang; Cui, Jing'an
2017-12-01
This paper studies the spread dynamics of a stochastic SIRS epidemic model with nonlinear incidence and varying population size, which is formulated as a piecewise deterministic Markov process. A threshold dynamic determined by the basic reproduction number R0 is established: the disease can be eradicated almost surely if R0 disease persists almost surely if R0 > 1. The existing method for analyzing ergodic behavior of population systems has been generalized. The modified method weakens the required conditions and has no limitations for both the number of environmental regimes and the dimension of the considered system. When R0 > 1, the existence of a stationary probability measure is obtained. Furthermore, with the modified method, the global attractivity of the Ω-limit set of the system and the convergence in total variation to the stationary measure are both demonstrated under a mild extra condition.
Directory of Open Access Journals (Sweden)
Saki Takahashi
2016-02-01
Full Text Available Hand, foot, and mouth disease (HFMD is a common childhood illness caused by serotypes of the Enterovirus A species in the genus Enterovirus of the Picornaviridae family. The disease has had a substantial burden throughout East and Southeast Asia over the past 15 y. China reported 9 million cases of HFMD between 2008 and 2013, with the two serotypes Enterovirus A71 (EV-A71 and Coxsackievirus A16 (CV-A16 being responsible for the majority of these cases. Three recent phase 3 clinical trials showed that inactivated monovalent EV-A71 vaccines manufactured in China were highly efficacious against HFMD associated with EV-A71, but offered no protection against HFMD caused by CV-A16. To better inform vaccination policy, we used mathematical models to evaluate the effect of prospective vaccination against EV-A71-associated HFMD and the potential risk of serotype replacement by CV-A16. We also extended the model to address the co-circulation, and implications for vaccination, of additional non-EV-A71, non-CV-A16 serotypes of enterovirus.Weekly reports of HFMD incidence from 31 provinces in Mainland China from 1 January 2009 to 31 December 2013 were used to fit multi-serotype time series susceptible-infected-recovered (TSIR epidemic models. We obtained good model fit for the two-serotype TSIR with cross-protection, capturing the seasonality and geographic heterogeneity of province-level transmission, with strong correlation between the observed and simulated epidemic series. The national estimate of the basic reproduction number, R0, weighted by provincial population size, was 26.63 for EV-A71 (interquartile range [IQR]: 23.14, 30.40 and 27.13 for CV-A16 (IQR: 23.15, 31.34, with considerable variation between provinces (however, predictions about the overall impact of vaccination were robust to this variation. EV-A71 incidence was projected to decrease monotonically with higher coverage rates of EV-A71 vaccination. Across provinces, CV-A16 incidence in the
Takahashi, Saki; Liao, Qiaohong; Van Boeckel, Thomas P; Xing, Weijia; Sun, Junling; Hsiao, Victor Y; Metcalf, C Jessica E; Chang, Zhaorui; Liu, Fengfeng; Zhang, Jing; Wu, Joseph T; Cowling, Benjamin J; Leung, Gabriel M; Farrar, Jeremy J; van Doorn, H Rogier; Grenfell, Bryan T; Yu, Hongjie
2016-02-01
Hand, foot, and mouth disease (HFMD) is a common childhood illness caused by serotypes of the Enterovirus A species in the genus Enterovirus of the Picornaviridae family. The disease has had a substantial burden throughout East and Southeast Asia over the past 15 y. China reported 9 million cases of HFMD between 2008 and 2013, with the two serotypes Enterovirus A71 (EV-A71) and Coxsackievirus A16 (CV-A16) being responsible for the majority of these cases. Three recent phase 3 clinical trials showed that inactivated monovalent EV-A71 vaccines manufactured in China were highly efficacious against HFMD associated with EV-A71, but offered no protection against HFMD caused by CV-A16. To better inform vaccination policy, we used mathematical models to evaluate the effect of prospective vaccination against EV-A71-associated HFMD and the potential risk of serotype replacement by CV-A16. We also extended the model to address the co-circulation, and implications for vaccination, of additional non-EV-A71, non-CV-A16 serotypes of enterovirus. Weekly reports of HFMD incidence from 31 provinces in Mainland China from 1 January 2009 to 31 December 2013 were used to fit multi-serotype time series susceptible-infected-recovered (TSIR) epidemic models. We obtained good model fit for the two-serotype TSIR with cross-protection, capturing the seasonality and geographic heterogeneity of province-level transmission, with strong correlation between the observed and simulated epidemic series. The national estimate of the basic reproduction number, R0, weighted by provincial population size, was 26.63 for EV-A71 (interquartile range [IQR]: 23.14, 30.40) and 27.13 for CV-A16 (IQR: 23.15, 31.34), with considerable variation between provinces (however, predictions about the overall impact of vaccination were robust to this variation). EV-A71 incidence was projected to decrease monotonically with higher coverage rates of EV-A71 vaccination. Across provinces, CV-A16 incidence in the post-EV-A71
Large-scale application of highly-diluted bacteria for Leptospirosis epidemic control.
Bracho, Gustavo; Varela, Enrique; Fernández, Rolando; Ordaz, Barbara; Marzoa, Natalia; Menéndez, Jorge; García, Luis; Gilling, Esperanza; Leyva, Richard; Rufín, Reynaldo; de la Torre, Rubén; Solis, Rosa L; Batista, Niurka; Borrero, Reinier; Campa, Concepción
2010-07-01
Leptospirosis is a zoonotic disease of major importance in the tropics where the incidence peaks in rainy seasons. Natural disasters represent a big challenge to Leptospirosis prevention strategies especially in endemic regions. Vaccination is an effective option but of reduced effectiveness in emergency situations. Homeoprophylactic interventions might help to control epidemics by using highly-diluted pathogens to induce protection in a short time scale. We report the results of a very large-scale homeoprophylaxis (HP) intervention against Leptospirosis in a dangerous epidemic situation in three provinces of Cuba in 2007. Forecast models were used to estimate possible trends of disease incidence. A homeoprophylactic formulation was prepared from dilutions of four circulating strains of Leptospirosis. This formulation was administered orally to 2.3 million persons at high risk in an epidemic in a region affected by natural disasters. The data from surveillance were used to measure the impact of the intervention by comparing with historical trends and non-intervention regions. After the homeoprophylactic intervention a significant decrease of the disease incidence was observed in the intervention regions. No such modifications were observed in non-intervention regions. In the intervention region the incidence of Leptospirosis fell below the historic median. This observation was independent of rainfall. The homeoprophylactic approach was associated with a large reduction of disease incidence and control of the epidemic. The results suggest the use of HP as a feasible tool for epidemic control, further research is warranted. 2010 Elsevier Ltd. All rights reserved.
Temporal prediction of epidemic patterns in community networks
International Nuclear Information System (INIS)
Peng, Xiao-Long; Xu, Xin-Jian; Fu, Xinchu; Small, Michael
2013-01-01
Most previous studies of epidemic dynamics on complex networks suppose that the disease will eventually stabilize at either a disease-free state or an endemic one. In reality, however, some epidemics always exhibit sporadic and recurrent behaviour in one region because of the invasion from an endemic population elsewhere. In this paper we address this issue and study a susceptible–infected–susceptible epidemiological model on a network consisting of two communities, where the disease is endemic in one community but alternates between outbreaks and extinctions in the other. We provide a detailed characterization of the temporal dynamics of epidemic patterns in the latter community. In particular, we investigate the time duration of both outbreak and extinction, and the time interval between two consecutive inter-community infections, as well as their frequency distributions. Based on the mean-field theory, we theoretically analyse these three timescales and their dependence on the average node degree of each community, the transmission parameters and the number of inter-community links, which are in good agreement with simulations, except when the probability of overlaps between successive outbreaks is too large. These findings aid us in better understanding the bursty nature of disease spreading in a local community, and thereby suggesting effective time-dependent control strategies. (paper)
The role of subway travel in an influenza epidemic: a New York City simulation.
Cooley, Philip; Brown, Shawn; Cajka, James; Chasteen, Bernadette; Ganapathi, Laxminarayana; Grefenstette, John; Hollingsworth, Craig R; Lee, Bruce Y; Levine, Burton; Wheaton, William D; Wagener, Diane K
2011-10-01
The interactions of people using public transportation in large metropolitan areas may help spread an influenza epidemic. An agent-based model computer simulation of New York City's (NYC's) five boroughs was developed that incorporated subway ridership into a Susceptible-Exposed-Infected-Recovered disease model framework. The model contains a total of 7,847,465 virtual people. Each person resides in one of the five boroughs of NYC and has a set of socio-demographic characteristics and daily behaviors that include age, sex, employment status, income, occupation, and household location and membership. The model simulates the interactions of subway riders with their workplaces, schools, households, and community activities. It was calibrated using historical data from the 1957-1958 influenza pandemics and from NYC travel surveys. The surveys were necessary to enable inclusion of subway riders into the model. The model results estimate that if influenza did occur in NYC with the characteristics of the 1957-1958 pandemic, 4% of transmissions would occur on the subway. This suggests that interventions targeted at subway riders would be relatively ineffective in containing the epidemic. A number of hypothetical examples demonstrate this feature. This information could prove useful to public health officials planning responses to epidemics.
The epidemic of methylisothiazolinone
DEFF Research Database (Denmark)
Schwensen, Jakob F; Uter, Wolfgang; Bruze, Magnus
2017-01-01
BACKGROUND: The use of methylisothiazolinone (MI) in cosmetic products has caused an unprecedented epidemic of MI contact allergy. Current data concerning exposures at a European level are required. OBJECTIVES: To describe demographics and MI exposures for European patients with MI contact allergy....... METHODS: Eleven European dermatology departments from eight European countries prospectively collected data between 1 May and 31 October 2015 among consecutive patients who had positive patch test reactions to MI (2000 ppm aq.). RESULTS: A total of 6.0% (205/3434; range 2.6-13.0%) of patients had positive...... patch test reactions to MI. Dermatitis most frequently affected the hands (43.4%), face (32.7%), arms (14.6%), and eyelids (11.7%); 12.7% had widespread dermatitis. For 72.7% (149/205), MI contact allergy was currently relevant mainly because of exposure to cosmetic products (83.2%; 124...
Teng, Zhidong; Wang, Lei
2016-06-01
In this paper, a class of stochastic SIS epidemic models with nonlinear incidence rate is investigated. It is shown that the extinction and persistence of the disease in probability are determined by a threshold value R˜0. That is, if R˜0 1 then disease is weak permanent with probability one. To obtain the permanence in the mean of the disease, a new quantity R̂0 is introduced, and it is proved that if R̂0 > 1 the disease is permanent in the mean with probability one. Furthermore, the numerical simulations are presented to illustrate some open problems given in Remarks 1-3 and 5 of this paper.
Influenza epidemics, seasonality, and the effects of cold weather on cardiac mortality
2012-01-01
Background More people die in the winter from cardiac disease, and there are competing hypotheses to explain this. The authors conducted a study in 48 US cities to determine how much of the seasonal pattern in cardiac deaths could be explained by influenza epidemics, whether that allowed a more parsimonious control for season than traditional spline models, and whether such control changed the short term association with temperature. Methods The authors obtained counts of daily cardiac deaths and of emergency hospital admissions of the elderly for influenza during 1992–2000. Quasi-Poisson regression models were conducted estimating the association between daily cardiac mortality, and temperature. Results Controlling for influenza admissions provided a more parsimonious model with better Generalized Cross-Validation, lower residual serial correlation, and better captured Winter peaks. The temperature-response function was not greatly affected by adjusting for influenza. The pooled estimated increase in risk for a temperature decrease from 0 to −5°C was 1.6% (95% confidence interval (CI) 1.1-2.1%). Influenza accounted for 2.3% of cardiac deaths over this period. Conclusions The results suggest that including epidemic data explained most of the irregular seasonal pattern (about 18% of the total seasonal variation), allowing more parsimonious models than when adjusting for seasonality only with smooth functions of time. The effect of cold temperature is not confounded by epidemics. PMID:23025494
Prevention of the Teenage Pregnancy Epidemic: A Social Learning Theory Approach.
Hagenhoff, Carol; And Others
1987-01-01
The review provides a social learning model for explaining adolescent sexual behavior and use/nonuse of contraceptives. The model explains behavior patterns responsible for epidemic rates of teenage pregnancies, suggests research that will result in prevention of teenage pregnancies, and incorporates a range of social/cultural factors. (DB)
Epidemic contact tracing via communication traces.
Directory of Open Access Journals (Sweden)
Katayoun Farrahi
Full Text Available Traditional contact tracing relies on knowledge of the interpersonal network of physical interactions, where contagious outbreaks propagate. However, due to privacy constraints and noisy data assimilation, this network is generally difficult to reconstruct accurately. Communication traces obtained by mobile phones are known to be good proxies for the physical interaction network, and they may provide a valuable tool for contact tracing. Motivated by this assumption, we propose a model for contact tracing, where an infection is spreading in the physical interpersonal network, which can never be fully recovered; and contact tracing is occurring in a communication network which acts as a proxy for the first. We apply this dual model to a dataset covering 72 students over a 9 month period, for which both the physical interactions as well as the mobile communication traces are known. Our results suggest that a wide range of contact tracing strategies may significantly reduce the final size of the epidemic, by mainly affecting its peak of incidence. However, we find that for low overlap between the face-to-face and communication interaction network, contact tracing is only efficient at the beginning of the outbreak, due to rapidly increasing costs as the epidemic evolves. Overall, contact tracing via mobile phone communication traces may be a viable option to arrest contagious outbreaks.
Epidemic contact tracing via communication traces.
Farrahi, Katayoun; Emonet, Rémi; Cebrian, Manuel
2014-01-01
Traditional contact tracing relies on knowledge of the interpersonal network of physical interactions, where contagious outbreaks propagate. However, due to privacy constraints and noisy data assimilation, this network is generally difficult to reconstruct accurately. Communication traces obtained by mobile phones are known to be good proxies for the physical interaction network, and they may provide a valuable tool for contact tracing. Motivated by this assumption, we propose a model for contact tracing, where an infection is spreading in the physical interpersonal network, which can never be fully recovered; and contact tracing is occurring in a communication network which acts as a proxy for the first. We apply this dual model to a dataset covering 72 students over a 9 month period, for which both the physical interactions as well as the mobile communication traces are known. Our results suggest that a wide range of contact tracing strategies may significantly reduce the final size of the epidemic, by mainly affecting its peak of incidence. However, we find that for low overlap between the face-to-face and communication interaction network, contact tracing is only efficient at the beginning of the outbreak, due to rapidly increasing costs as the epidemic evolves. Overall, contact tracing via mobile phone communication traces may be a viable option to arrest contagious outbreaks.
Topographic determinants of foot and mouth disease transmission in the UK 2001 epidemic
Directory of Open Access Journals (Sweden)
Keeling Matthew J
2006-01-01
Full Text Available Abstract Background A key challenge for modelling infectious disease dynamics is to understand the spatial spread of infection in real landscapes. This ideally requires a parallel record of spatial epidemic spread and a detailed map of susceptible host density along with relevant transport links and geographical features. Results Here we analyse the most detailed such data to date arising from the UK 2001 foot and mouth epidemic. We show that Euclidean distance between infectious and susceptible premises is a better predictor of transmission risk than shortest and quickest routes via road, except where major geographical features intervene. Conclusion Thus, a simple spatial transmission kernel based on Euclidean distance suffices in most regions, probably reflecting the multiplicity of transmission routes during the epidemic.
Epidemic spreading in weighted networks: an edge-based mean-field solution.
Yang, Zimo; Zhou, Tao
2012-05-01
Weight distribution greatly impacts the epidemic spreading taking place on top of networks. This paper presents a study of a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation results show that the more homogeneous weight distribution leads to higher epidemic prevalence, which, unfortunately, could not be captured by the traditional mean-field approximation. This paper gives an edge-based mean-field solution for general weight distribution, which can quantitatively reproduce the simulation results. This method could be applied to characterize the nonequilibrium steady states of dynamical processes on weighted networks.
Hybrid Epidemics - A Case Study on Computer Worm Conficker
Zhang, Changwang; Zhou, Shi; Chain, Benjamin M.
2014-01-01
Conficker is a computer worm that erupted on the Internet in 2008. It is unique in combining three different spreading strategies: local probing, neighbourhood probing, and global probing. We propose a mathematical model that combines three modes of spreading: local, neighbourhood, and global, to capture the worm's spreading behaviour. The parameters of the model are inferred directly from network data obtained during the first day of the Conficker epidemic. The model is then used to explore ...
Monitoring linked epidemics: the case of tuberculosis and HIV.
Directory of Open Access Journals (Sweden)
María S Sánchez
Full Text Available BACKGROUND: The tight epidemiological coupling between HIV and its associated opportunistic infections leads to challenges and opportunities for disease surveillance. METHODOLOGY/PRINCIPAL FINDINGS: We review efforts of WHO and collaborating agencies to track and fight the TB/HIV co-epidemic, and discuss modeling--via mathematical, statistical, and computational approaches--as a means to identify disease indicators designed to integrate data from linked diseases in order to characterize how co-epidemics change in time and space. We present R(TB/HIV, an index comparing changes in TB incidence relative to HIV prevalence, and use it to identify those sub-Saharan African countries with outlier TB/HIV dynamics. R(TB/HIV can also be used to predict epidemiological trends, investigate the coherency of reported trends, and cross-check the anticipated impact of public health interventions. Identifying the cause(s responsible for anomalous R(TB/HIV values can reveal information crucial to the management of public health. CONCLUSIONS/SIGNIFICANCE: We frame our suggestions for integrating and analyzing co-epidemic data within the context of global disease monitoring. Used routinely, joint disease indicators such as R(TB/HIV could greatly enhance the monitoring and evaluation of public health programs.
Epidemics: Lessons from the past and current patterns of response
Martin, Paul
2008-09-01
Hippocrates gave the term 'epidemic' its medical meaning. From antiquity to modern times, the meaning of the word epidemic has continued to evolve. Over the centuries, researchers have reached an understanding of the varying aspects of epidemics and have tried to combat them. The role played by travel, trade, and human exchanges in the propagation of epidemic infectious diseases has been understood. In 1948, the World Health Organization was created and given the task of advancing ways of combating epidemics. An early warning system to combat epidemics has been implemented by the WHO. The Global Outbreak Alert and Response Network (GOARN) is collaboration between existing institutions and networks that pool their human and technical resources to fight outbreaks. Avian influenza constitutes currently the most deadly epidemic threat, with fears that it could rapidly reach pandemic proportions and put several thousands of lives in jeopardy. Thanks to the WHO's support, most of the world's countries have mobilised and implemented an 'Action Plan for Pandemic Influenza'. As a result, most outbreaks of the H5N1 avian flu virus have so far been speedily contained. Cases of dengue virus introduction in countries possessing every circumstance required for its epidemic spread provide another example pertinent to the prevention of epidemics caused by vector-borne pathogens.
A Kinetic Model Describing Injury-Burden in Team Sports.
Fuller, Colin W
2017-12-01
Injuries in team sports are normally characterised by the incidence, severity, and location and type of injuries sustained: these measures, however, do not provide an insight into the variable injury-burden experienced during a season. Injury burden varies according to the team's match and training loads, the rate at which injuries are sustained and the time taken for these injuries to resolve. At the present time, this time-based variation of injury burden has not been modelled. To develop a kinetic model describing the time-based injury burden experienced by teams in elite team sports and to demonstrate the model's utility. Rates of injury were quantified using a large eight-season database of rugby injuries (5253) and exposure (60,085 player-match-hours) in English professional rugby. Rates of recovery from injury were quantified using time-to-recovery analysis of the injuries. The kinetic model proposed for predicting a team's time-based injury burden is based on a composite rate equation developed from the incidence of injury, a first-order rate of recovery from injury and the team's playing load. The utility of the model was demonstrated by examining common scenarios encountered in elite rugby. The kinetic model developed describes and predicts the variable injury-burden arising from match play during a season of rugby union based on the incidence of match injuries, the rate of recovery from injury and the playing load. The model is equally applicable to other team sports and other scenarios.
Dynamical behavior of an epidemic model for a vector-borne disease with direct transmission
International Nuclear Information System (INIS)
Cai Liming; Li Xuezhi; Li Zhaoqiang
2013-01-01
An epidemic model of a vector-borne disease with direct transmission is investigated. The reproduction number (R 0 ) of the model is obtained. Rigorous qualitative analysis of the model reveals the presence of the phenomenon of backward bifurcation (where the stable disease-free equilibrium (DFE) coexists with a stable endemic equilibrium when the reproduction number of the disease is less than unity) in the standard incidence model. The phenomenon shows that the classical epidemiological requirement of having the reproduction number less than unity is no longer sufficient, although necessary, for effectively controlling the spread of some vector-borne diseases in a community. The backward bifurcation phenomenon can be removed by substituting the standard incidence with a bilinear mass action incidence. By using Lyapunov function theory and LaSalle invariance principle, it is shown that the unique endemic equilibrium for the model with a mass action incidence is globally stable if the reproduction number R mass is greater than one in feasible region. This suggests that the use of standard incidence in modelling some vector-borne diseases with direct transmission results in the presence of backward bifurcation. Numerical simulations analyze the effect of the direct transmission and the disease-induced death rate on dynamics of the disease transmission, and also verify our analyzed results.
Stochastic analysis of a novel nonautonomous periodic SIRI epidemic system with random disturbances
Zhang, Weiwei; Meng, Xinzhu
2018-02-01
In this paper, a new stochastic nonautonomous SIRI epidemic model is formulated. Given that the incidence rates of diseases may change with the environment, we propose a novel type of transmission function. The main aim of this paper is to obtain the thresholds of the stochastic SIRI epidemic model. To this end, we investigate the dynamics of the stochastic system and establish the conditions for extinction and persistence in mean of the disease by constructing some suitable Lyapunov functions and using stochastic analysis technique. Furthermore, we show that the stochastic system has at least one nontrivial positive periodic solution. Finally, numerical simulations are introduced to illustrate our results.
Epidemic threshold in directed networks
Li, Cong; Wang, Huijuan; Van Mieghem, Piet
2013-12-01
Epidemics have so far been mostly studied in undirected networks. However, many real-world networks, such as the online social network Twitter and the world wide web, on which information, emotion, or malware spreads, are directed networks, composed of both unidirectional links and bidirectional links. We define the directionality ξ as the percentage of unidirectional links. The epidemic threshold τc for the susceptible-infected-susceptible (SIS) epidemic is lower bounded by 1/λ1 in directed networks, where λ1, also called the spectral radius, is the largest eigenvalue of the adjacency matrix. In this work, we propose two algorithms to generate directed networks with a given directionality ξ. The effect of ξ on the spectral radius λ1, principal eigenvector x1, spectral gap (λ1-λ2), and algebraic connectivity μN-1 is studied. Important findings are that the spectral radius λ1 decreases with the directionality ξ, whereas the spectral gap and the algebraic connectivity increase with the directionality ξ. The extent of the decrease of the spectral radius depends on both the degree distribution and the degree-degree correlation ρD. Hence, in directed networks, the epidemic threshold is larger and a random walk converges to its steady state faster than that in undirected networks with the same degree distribution.
The influence of the school year on measles epidemics
DEFF Research Database (Denmark)
Andreasen, Viggo
The measles incidence record for Copenhagen 1880-1966 shows that the date of admission of new pupils has major impact on the structure of the epidemics, suggesting that measles transmission should be modelled in a way that accounts for the pulsed influx of new pupils. Assuming that the school year...
Using data-driven agent-based models for forecasting emerging infectious diseases
Directory of Open Access Journals (Sweden)
Srinivasan Venkatramanan
2018-03-01
Full Text Available Producing timely, well-informed and reliable forecasts for an ongoing epidemic of an emerging infectious disease is a huge challenge. Epidemiologists and policy makers have to deal with poor data quality, limited understanding of the disease dynamics, rapidly changing social environment and the uncertainty on effects of various interventions in place. Under this setting, detailed computational models provide a comprehensive framework for integrating diverse data sources into a well-defined model of disease dynamics and social behavior, potentially leading to better understanding and actions. In this paper, we describe one such agent-based model framework developed for forecasting the 2014–2015 Ebola epidemic in Liberia, and subsequently used during the Ebola forecasting challenge. We describe the various components of the model, the calibration process and summarize the forecast performance across scenarios of the challenge. We conclude by highlighting how such a data-driven approach can be refined and adapted for future epidemics, and share the lessons learned over the course of the challenge. Keywords: Emerging infectious diseases, Agent-based models, Simulation optimization, Bayesian calibration, Ebola
Blake, Alexandre; Keita, Veronique Sarr; Sauvageot, Delphine; Saliou, Mamadou; Njanpop, Berthe Marie; Sory, Fode; Sudre, Bertrand; Lamine, Koivogui; Mengel, Martin; Gessner, Bradford D; Sakoba, Keita
2018-02-15
Cholera is endemic in Guinea, having suffered consecutive outbreaks from 2004 to 2008 followed by a lull until the 2012 epidemic. Here we describe the temporal-spatial and behavioural characteristics of cholera cases in Conakry during a three-year period, including the large-scale 2012 epidemic. We used the national and African Cholera Surveillance Network (Africhol) surveillance data collected from every cholera treatment centre in Conakry city from August 2011 to December 2013. The prevalence of suspect and confirmed cholera cases, the case fatality ratio (CFR), and the factors associated with suspected cholera were described according to three periods: pre-epidemic (A), epidemic 2012 (B) and post epidemic (C). Weekly attack rates and temporal-spatial clustering were calculated at municipality level for period B. Cholera was confirmed by culture at the cholera national reference laboratory. A total of 4559 suspect cases were reported: 66, 4437, and 66 suspect cases in periods A, B and C, respectively. Among the 204 suspect cases with culture results available, 6%, 60%, and 70% were confirmed in periods A, B, and C, respectively. With 0.3%, the CFR was significantly lower in period B than in periods A (7.6%) and C (7.1%). The overall attack rate was 0.28% in period B, ranging from 0.17% to 0.31% across municipalities. Concomitantly, a cluster of cases was identified in two districts in the northern part of Conakry. At 14%, rice water stools were less frequent in period A than in period B and C (78% and 84%). Dehydration (31% vs 94% and 89%) and coma (0.4% vs 3.1% and 2.9%) were lower during period B than in periods A and C. The treatment of drinking water was less frequent in period A, while there were more reports of recent travel in period C. The epidemic dynamic and the sociological description of suspect cases before, during, and after the large-scale epidemic revealed that the Vibrio cholerae was already present before the epidemic. However, it appeared that
Stochastic analysis of epidemics on adaptive time varying networks
Kotnis, Bhushan; Kuri, Joy
2013-06-01
Many studies investigating the effect of human social connectivity structures (networks) and human behavioral adaptations on the spread of infectious diseases have assumed either a static connectivity structure or a network which adapts itself in response to the epidemic (adaptive networks). However, human social connections are inherently dynamic or time varying. Furthermore, the spread of many infectious diseases occur on a time scale comparable to the time scale of the evolving network structure. Here we aim to quantify the effect of human behavioral adaptations on the spread of asymptomatic infectious diseases on time varying networks. We perform a full stochastic analysis using a continuous time Markov chain approach for calculating the outbreak probability, mean epidemic duration, epidemic reemergence probability, etc. Additionally, we use mean-field theory for calculating epidemic thresholds. Theoretical predictions are verified using extensive simulations. Our studies have uncovered the existence of an “adaptive threshold,” i.e., when the ratio of susceptibility (or infectivity) rate to recovery rate is below the threshold value, adaptive behavior can prevent the epidemic. However, if it is above the threshold, no amount of behavioral adaptations can prevent the epidemic. Our analyses suggest that the interaction patterns of the infected population play a major role in sustaining the epidemic. Our results have implications on epidemic containment policies, as awareness campaigns and human behavioral responses can be effective only if the interaction levels of the infected populace are kept in check.
Effects of local and global network connectivity on synergistic epidemics
Broder-Rodgers, David; Pérez-Reche, Francisco J.; Taraskin, Sergei N.
2015-12-01
Epidemics in networks can be affected by cooperation in transmission of infection and also connectivity between nodes. An interplay between these two properties and their influence on epidemic spread are addressed in the paper. A particular type of cooperative effects (called synergy effects) is considered, where the transmission rate between a pair of nodes depends on the number of infected neighbors. The connectivity effects are studied by constructing networks of different topology, starting with lattices with only local connectivity and then with networks that have both local and global connectivity obtained by random bond-rewiring to nodes within a certain distance. The susceptible-infected-removed epidemics were found to exhibit several interesting effects: (i) for epidemics with strong constructive synergy spreading in networks with high local connectivity, the bond rewiring has a negative role in epidemic spread, i.e., it reduces invasion probability; (ii) in contrast, for epidemics with destructive or weak constructive synergy spreading on networks of arbitrary local connectivity, rewiring helps epidemics to spread; (iii) and, finally, rewiring always enhances the spread of epidemics, independent of synergy, if the local connectivity is low.
Fumanelli, Laura; Ajelli, Marco; Merler, Stefano; Ferguson, Neil M; Cauchemez, Simon
2016-01-01
School closure policies are among the non-pharmaceutical measures taken into consideration to mitigate influenza epidemics and pandemics spread. However, a systematic review of the effectiveness of alternative closure policies has yet to emerge. Here we perform a model-based analysis of four types of school closure, ranging from the nationwide closure of all schools at the same time to reactive gradual closure, starting from class-by-class, then grades and finally the whole school. We consider policies based on triggers that are feasible to monitor, such as school absenteeism and national ILI surveillance system. We found that, under specific constraints on the average number of weeks lost per student, reactive school-by-school, gradual, and county-wide closure give comparable outcomes in terms of optimal infection attack rate reduction, peak incidence reduction or peak delay. Optimal implementations generally require short closures of one week each; this duration is long enough to break the transmission chain without leading to unnecessarily long periods of class interruption. Moreover, we found that gradual and county closures may be slightly more easily applicable in practice as they are less sensitive to the value of the excess absenteeism threshold triggering the start of the intervention. These findings suggest that policy makers could consider school closure policies more diffusely as response strategy to influenza epidemics and pandemics, and the fact that some countries already have some experience of gradual or regional closures for seasonal influenza outbreaks demonstrates that logistic and feasibility challenges of school closure strategies can be to some extent overcome.
Abia State HIV epidemic and response: challenges and prospects.
Onyeonoro, Ugochukwu Uchenna; Emelumadu, Obiageli Fidelia; Nwamoh, Uche Ngozi; Ukegbu, Andrew Ugwunna; Okafor, Godwin Oc
2014-11-13
Since the first seroprevalence survey in 1999, the HIV prevalence in Abia State has increased from 1.8% to 7.3% in 2010. The state is currently experiencing a generalized epidemic, with most transmission occurring through heterosexual low-risk sex. Drivers of the epidemic include low knowledge of HIV prevention, low risk perception, predominantly male factor-driven risky sexual behavior, and low condom use. This study reviewed the state HIV epidemic trend in relation to response, sought to identify the gaps between the epidemic and response, and recommended measures to strengthen the state response.
Optimal Control of Interdependent Epidemics in Complex Networks
Chen, Juntao; Zhang, Rui; Zhu, Quanyan
2017-01-01
Optimal control of interdependent epidemics spreading over complex networks is a critical issue. We first establish a framework to capture the coupling between two epidemics, and then analyze the system's equilibrium states by categorizing them into three classes, and deriving their stability conditions. The designed control strategy globally optimizes the trade-off between the control cost and the severity of epidemics in the network. A gradient descent algorithm based on a fixed point itera...
Directory of Open Access Journals (Sweden)
Omori Ryosuke
2011-01-01
Full Text Available Abstract Background While many pandemic preparedness plans have promoted disease control effort to lower and delay an epidemic peak, analytical methods for determining the required control effort and making statistical inferences have yet to be sought. As a first step to address this issue, we present a theoretical basis on which to assess the impact of an early intervention on the epidemic peak, employing a simple epidemic model. Methods We focus on estimating the impact of an early control effort (e.g. unsuccessful containment, assuming that the transmission rate abruptly increases when control is discontinued. We provide analytical expressions for magnitude and time of the epidemic peak, employing approximate logistic and logarithmic-form solutions for the latter. Empirical influenza data (H1N1-2009 in Japan are analyzed to estimate the effect of the summer holiday period in lowering and delaying the peak in 2009. Results Our model estimates that the epidemic peak of the 2009 pandemic was delayed for 21 days due to summer holiday. Decline in peak appears to be a nonlinear function of control-associated reduction in the reproduction number. Peak delay is shown to critically depend on the fraction of initially immune individuals. Conclusions The proposed modeling approaches offer methodological avenues to assess empirical data and to objectively estimate required control effort to lower and delay an epidemic peak. Analytical findings support a critical need to conduct population-wide serological survey as a prior requirement for estimating the time of peak.
Acute hemorrhagic conjunctivitis epidemic in São Paulo State, Brazil, 2011
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Norma H. Medina
Full Text Available ABSTRACT Acute hemorrhagic conjunctivitis (AHC infection is highly contagious and can lead to explosive epidemics. In early February 2011, the Center for Epidemiologic Surveillance of the State of São Paulo Health Secretariat (SES-SP in Brazil received reports of conjunctivitis outbreaks from rural areas of the state that subsequently spread statewide. This report describes that AHC epidemic and its etiologic agent. Data from the Ministry of Health Information System for Notifiable Diseases (SinanNet and the SES-SP epidemiologic surveillance system for conjunctivitis, developed to detect outbreaks, confirm the etiologic agent, and carry out control measures, were analyzed. Eye (conjunctival swab samples were taken from patients with clinical presentation of viral conjunctivitis to perform viral laboratory diagnosis. A total of 1 067 981 conjunctivitis cases were reported to the surveillance system for 2011; there was an increase in the number of cases in epidemiologic weeks 6–26 (summer season versus previous years. Most cases occurred in the metropolitan region of Greater São Paulo. Of 93 collected samples, 57 tested positive for coxsackievirus-A24 (CV-A24, based on virus isolation in tissue-culture cell lines, reverse transcription polymerase chain reaction (RT-PCR, and enterovirus sequencing of RT-PCR. The data analysis showed that the fast-spreading etiologic agent of the AHC epidemic that occurred in the summer of 2011 was CV-A24. The AHC epidemic was due to an enterovirus that occurred sporadically, spread rapidly and with great magnitude, and had substantial socioeconomic impact due to the high level of absenteeism at work and school.
Percolation and epidemics in random clustered networks
Miller, Joel C.
2009-08-01
The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease dynamics. A number of authors have studied percolation or epidemics in clustered networks, but the networks often contain preferential contacts in high degree nodes. We introduce a class of random clustered networks and a class of random unclustered networks with the same preferential mixing. Percolation in the clustered networks reduces the component sizes and increases the epidemic threshold compared to the unclustered networks.
Landscape changes in the environment due to military actions and their epidemic risks
Directory of Open Access Journals (Sweden)
Krushelnitsky A.D.
2016-05-01
Full Text Available The article considers the influence of the military-ecological and man-caused-anthropogenic factors on the environment state and natural processes. Epidemic risks and consequences resulted from landscapic changes of the environment which arise as a result of war and destruction of ecosystems are described.
Suppressing traffic-driven epidemic spreading by adaptive routing strategy
International Nuclear Information System (INIS)
Yang, Han-Xin; Wang, Zhen
2016-01-01
The design of routing strategies for traffic-driven epidemic spreading has received increasing attention in recent years. In this paper, we propose an adaptive routing strategy that incorporates topological distance with local epidemic information through a tunable parameter h. In the case where the traffic is free of congestion, there exists an optimal value of routing parameter h, leading to the maximal epidemic threshold. This means that epidemic spreading can be more effectively controlled by adaptive routing, compared to that of the static shortest path routing scheme. Besides, we find that the optimal value of h can greatly relieve the traffic congestion in the case of finite node-delivering capacity. We expect our work to provide new insights into the effects of dynamic routings on traffic-driven epidemic spreading.
George, Janet L; Martin, Daniel J; Lukacs, Paul M; Miller, Michael W
2008-04-01
A pneumonia epidemic reduced bighorn sheep (Ovis canadensis) survival and recruitment during 1997-2000 in a population comprised of three interconnected wintering herds (Kenosha Mountains, Sugarloaf Mountain, Twin Eagles) that inhabited the Kenosha and Tarryall Mountain ranges in central Colorado, USA. The onset of this epidemic coincided temporally and spatially with the appearance of a single domestic sheep (Ovis aires) on the Sugarloaf Mountain herd's winter range in December 1997. Although only bighorns in the Sugarloaf Mountain herd were affected in 1997-98, cases also occurred during 1998-99 in the other two wintering herds, likely after the epidemic spread via established seasonal movements of male bighorns. In all, we located 86 bighorn carcasses during 1997-2000. Three species of Pasteurella were isolated in various combinations from affected lung tissues from 20 bighorn carcasses where tissues were available and suitable for diagnostic evaluation; with one exception, beta-hemolytic mannheimia (Pasteurella) haemolytica (primarily reported as biogroup 1(G) or 1(alphaG)) was isolated from lung tissues of cases evaluated during winter 1997-98. The epidemic dramatically lowered adult bighorn monthly survival in all three herds; a model that included an acute epidemic effect, differing between sexes and with vaccination status, that diminished linearly over the next 12 mo best represented field data. In addition to the direct mortality associated with epidemics in these three herds, lamb recruitment in years following the pneumonia epidemic also was depressed as compared to years prior to the epidemic. Based on observations presented here, pasteurellosis epidemics in free-ranging bighorn sheep can arise through incursion of domestic sheep onto native ranges, and thus minimizing contact between domestic and bighorn sheep appears to be a logical principle for bighorn sheep conservation.
Evolution of scaling emergence in large-scale spatial epidemic spreading.
Wang, Lin; Li, Xiang; Zhang, Yi-Qing; Zhang, Yan; Zhang, Kan
2011-01-01
Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified. In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence. The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.
Models for describing the thermal characteristics of building components
DEFF Research Database (Denmark)
Jimenez, M.J.; Madsen, Henrik
2008-01-01
, for example. For the analysis of these tests, dynamic analysis models and methods are required. However, a wide variety of models and methods exists, and the problem of choosing the most appropriate approach for each particular case is a non-trivial and interdisciplinary task. Knowledge of a large family....... The characteristics of each type of model are highlighted. Some available software tools for each of the methods described will be mentioned. A case study also demonstrating the difference between linear and nonlinear models is considered....... of these approaches may therefore be very useful for selecting a suitable approach for each particular case. This paper presents an overview of models that can be applied for modelling the thermal characteristics of buildings and building components using data from outdoor testing. The choice of approach depends...
Ceccato, Pietro; Vancutsem, Christelle; Klaver, Robert; Rowland, James; Connor, Stephen J.
2012-01-01
Rainfall and temperature are two of the major factors triggering malaria epidemics in warm semi-arid (desert-fringe) and high altitude (highland-fringe) epidemic risk areas. The ability of the mosquitoes to transmit Plasmodium spp. is dependent upon a series of biological features generally referred to as vectorial capacity. In this study, the vectorial capacity model (VCAP) was expanded to include the influence of rainfall and temperature variables on malaria transmission potential. Data from two remote sensing products were used to monitor rainfall and temperature and were integrated into the VCAP model. The expanded model was tested in Eritrea and Madagascar to check the viability of the approach. The analysis of VCAP in relation to rainfall, temperature and malaria incidence data in these regions shows that the expanded VCAP correctly tracks the risk of malaria both in regions where rainfall is the limiting factor and in regions where temperature is the limiting factor. The VCAP maps are currently offered as an experimental resource for testing within Malaria Early Warning applications in epidemic prone regions of sub-Saharan Africa. User feedback is currently being collected in preparation for further evaluation and refinement of the VCAP model.
Epidemics and dimensionality in hierarchical networks
Zheng, Da-Fang; Hui, P. M.; Trimper, Steffen; Zheng, Bo
2005-07-01
Epidemiological processes are studied within a recently proposed hierarchical network model using the susceptible-infected-refractory dynamics of an epidemic. Within the network model, a population may be characterized by H independent hierarchies or dimensions, each of which consists of groupings of individuals into layers of subgroups. Detailed numerical simulations reveal that for H>1, global spreading results regardless of the degree of homophily of the individuals forming a social circle. For H=1, a transition from global to local spread occurs as the population becomes decomposed into increasingly homophilous groups. Multiple dimensions in classifying individuals (nodes) thus make a society (computer network) highly susceptible to large-scale outbreaks of infectious diseases (viruses).
Dynamics of epidemic spreading with vaccination: Impact of social pressure and engagement
Pires, Marcelo A.; Crokidakis, Nuno
2017-02-01
In this work we consider a model of epidemic spreading coupled with an opinion dynamics in a fully-connected population. Regarding the opinion dynamics, the individuals may be in two distinct states, namely in favor or against a vaccination campaign. Individuals against the vaccination follow a standard SIS model, whereas the pro-vaccine individuals can also be in a third compartment, namely Vaccinated. In addition, the opinions change according to the majority-rule dynamics in groups with three individuals. We also consider that the vaccine can give permanent or temporary immunization to the individuals. By means of analytical calculations and computer simulations, we show that the opinion dynamics can drastically affect the disease propagation, and that the engagement of the pro-vaccine individuals can be crucial for stopping the epidemic spreading. The full numerical code for simulating the model is available from the authors' webpage.
Centers for Disease Control (CDC) Podcasts
2011-07-18
Learn about obesity and the community initiatives taking place to prevent and reduce this epidemic. Created: 7/18/2011 by National Center for Chronic Disease Prevention and Health Promotion, Division of Nutrition, Physical Activity and Obesity. Date Released: 7/18/2011.
A Bayesian method for inferring transmission chains in a partially observed epidemic.
Energy Technology Data Exchange (ETDEWEB)
Marzouk, Youssef M.; Ray, Jaideep
2008-10-01
We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historical data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.
Effects of epidemic threshold definition on disease spread statistics
Lagorio, C.; Migueles, M. V.; Braunstein, L. A.; López, E.; Macri, P. A.
2009-03-01
We study the statistical properties of SIR epidemics in random networks, when an epidemic is defined as only those SIR propagations that reach or exceed a minimum size sc. Using percolation theory to calculate the average fractional size of an epidemic, we find that the strength of the spanning link percolation cluster P∞ is an upper bound to . For small values of sc, P∞ is no longer a good approximation, and the average fractional size has to be computed directly. We find that the choice of sc is generally (but not always) guided by the network structure and the value of T of the disease in question. If the goal is to always obtain P∞ as the average epidemic size, one should choose sc to be the typical size of the largest percolation cluster at the critical percolation threshold for the transmissibility. We also study Q, the probability that an SIR propagation reaches the epidemic mass sc, and find that it is well characterized by percolation theory. We apply our results to real networks (DIMES and Tracerouter) to measure the consequences of the choice sc on predictions of average outcome sizes of computer failure epidemics.
Tuckwell, H C; Toubiana, L; Vibert, J F
2000-05-01
We extend a previous dynamical viral network model to include stochastic effects. The dynamical equations for the viral and immune effector densities within a host population of size n are bilinear, and the noise is white, additive, and Gaussian. The individuals are connected with an n x n transmission matrix, with terms which decay exponentially with distance. In a single individual, for the range of noise parameters considered, it is found that increasing the amplitude of the noise tends to decrease the maximum mean virion level, and slightly accelerate its attainment. Two different spatial dynamical models are employed to ascertain the effects of environmental stochasticity on viral spread. In the first model transmission is unrestricted and there is no threshold within individuals. This model has the advantage that it can be analyzed using a Fokker-Planck approach. The noise is found both to synchronize and uniformize the trajectories of the viral levels across the population of infected individuals, and thus to promote the epidemic spread of the virus. Quantitative measures of the speed of spread and overall amplitude of the epidemic are obtained as functions of the noise and virulence parameters. The mean amplitude increases steadily without threshold effects for a fixed value of the virulence as the noise amplitude sigma is increased, and there is no evidence of a stochastic resonance. However, the speed of transmission, both with respect to its mean and variance, undergoes rapid increases as sigma changes by relatively small amounts. In the second, more realistic, model, there is a threshold for infection and an upper limit to the transmission rate. There may be no spread of infection at all in the absence of noise. With increasing noise level and a low threshold, the mean maximum virion level grows quickly and shows a broad-based stochastic resonance effect. When the threshold within individuals is increased, the mean population virion level increases only
The narcissism epidemic is dead : Long live the narcissism epidemic
Wetzel, Eunike; Brown, Anna; Hill, Patrick; Chung, J.M.H.; Robins, R.W.; Roberts, B.W.
2017-01-01
Are recent cohorts of college students more narcissistic than their predecessors? To address debates about the so-called “narcissism epidemic,” we used data from three cohorts of students (N1990s = 1,166; N2000s = 33,647; N2010s = 25,412) to test whether narcissism levels (overall and specific
Eisele, M; Hansen, H; Wagner, H-O; von Leitner, E; Pohontsch, N; Scherer, M
2014-06-01
As primary care givers with a coordinating function, general practitioners (GP) play a key role in dealing with epidemics and pandemics. As of yet, there are no studies in Germany describing the difficulties experienced by GPs in patient care during epidemics/pandemics. This study aimed at identifying the problem areas in GPs' patient care during the H1N1 and EHEC (enterohemorrhagic strain of Escherichia coli) outbreaks. With this information, recommendations for guaranteeing proper patient care during future epidemics/pandemics can be derived. In all, 12 qualitative, semi-structured, open guideline interviews with GPs in Hamburg and Lübeck were conducted, transcribed, and evaluated with qualitative content analysis. Five areas in ambulatory patient care were identified in which changes are needed from the primary care perspective: provision of information for GPs, workload, financing of epidemic-related measures, organization of the practices, care of those taken ill. The workload of GPs in particular can and should be reduced through successful, centralized information distribution during epidemics/pandemics. The GP's function as a coordinator should be supported and consolidated, in order to relieve the in-patient sector in cases of an epidemic/pandemic. Secured financing of epidemic-associated measures can help ensure patient care.
Nandi, Swapan Kumar; Jana, Soovoojeet; Mandal, Manotosh; Kar, T. K.
In this paper, we proposed and analyzed a susceptible-infected-recovered (SIR) type epidemic model to investigate the effect of transport-related infectious diseases namely tuberculosis, measles, rubella, influenza, sexually transmitted diseases, etc. The existence and stability criteria of both the diseases include free equilibrium point and endemic equilibrium point which are established and the threshold parametric condition for which the system passes through a transcritical bifurcation is also obtained. Optimal control strategy for control parameters is formulated and solved both theoretically and numerically. Lastly, we not only illustrate our theoretical results through graphical illustrations but also computer simulation is used to show that our model would be a good model to study the SARS epidemic in 2003.
Modeling of contact tracing in social networks
Tsimring, Lev S.; Huerta, Ramón
2003-07-01
Spreading of certain infections in complex networks is effectively suppressed by using intelligent strategies for epidemic control. One such standard epidemiological strategy consists in tracing contacts of infected individuals. In this paper, we use a recently introduced generalization of the standard susceptible-infectious-removed stochastic model for epidemics in sparse random networks which incorporates an additional (traced) state. We describe a deterministic mean-field description which yields quantitative agreement with stochastic simulations on random graphs. We also discuss the role of contact tracing in epidemics control in small-world and scale-free networks. Effectiveness of contact tracing grows as the rewiring probability is reduced.
African Journals Online (AJOL)
frequently brings shame, fear and guilt: dealing with this for some will begin a process of .... 'AZT treatment will have a limited effect on the epidemic, as we are targeting ... others to make the decisions that control my life. It is ironic that a society ...
Deep assessment: an exploratory study of game-based, multimodal learning in Epidemic
Directory of Open Access Journals (Sweden)
Jennifer Jenson
2016-03-01
Full Text Available n this study, we examine what and how intermediate age students learned from playing in a health-focused game-based digital learning environment, Epidemic. Epidemic is a playful interactive environment designed to deliver factual knowledge, invite critical understanding, and encourage effective self-care practices in dealing with viral contagious diseases, using a social networking interface to integrate both serious games and game-like multimodal design projects. Epidemic invites a playful approach to its deadly serious core concern – communicable disease – in order to see what happens when students are encouraged to critically approach information from multiple or contradictory perspectives. To identify what participants learned while interacting within Epidemic, we deployed two instructional and assessment models, noting the differences each instructional approach could potentially make, and what approach to assessment might help us evaluate game-based learning. We found that each approach provided importantly different perspectives on what and how students learned, and on the very meaning of student success. Recognizing that traditional assessment tools based in print-cultural literacy may prove increasingly ill-suited for assessing emergent multimodal literacies in game-based learning environments, this study seeks to contribute to a growing body of work on the development of novel assessments for learning.
Dynamical Interplay between Awareness and Epidemic Spreading in Multiplex Networks
Granell, Clara; Gómez, Sergio; Arenas, Alex
2013-09-01
We present the analysis of the interrelation between two processes accounting for the spreading of an epidemic, and the information awareness to prevent its infection, on top of multiplex networks. This scenario is representative of an epidemic process spreading on a network of persistent real contacts, and a cyclic information awareness process diffusing in the network of virtual social contacts between the same individuals. The topology corresponds to a multiplex network where two diffusive processes are interacting affecting each other. The analysis using a microscopic Markov chain approach reveals the phase diagram of the incidence of the epidemics and allows us to capture the evolution of the epidemic threshold depending on the topological structure of the multiplex and the interrelation with the awareness process. Interestingly, the critical point for the onset of the epidemics has a critical value (metacritical point) defined by the awareness dynamics and the topology of the virtual network, from which the onset increases and the epidemics incidence decreases.
Dynamical interplay between awareness and epidemic spreading in multiplex networks.
Granell, Clara; Gómez, Sergio; Arenas, Alex
2013-09-20
We present the analysis of the interrelation between two processes accounting for the spreading of an epidemic, and the information awareness to prevent its infection, on top of multiplex networks. This scenario is representative of an epidemic process spreading on a network of persistent real contacts, and a cyclic information awareness process diffusing in the network of virtual social contacts between the same individuals. The topology corresponds to a multiplex network where two diffusive processes are interacting affecting each other. The analysis using a microscopic Markov chain approach reveals the phase diagram of the incidence of the epidemics and allows us to capture the evolution of the epidemic threshold depending on the topological structure of the multiplex and the interrelation with the awareness process. Interestingly, the critical point for the onset of the epidemics has a critical value (metacritical point) defined by the awareness dynamics and the topology of the virtual network, from which the onset increases and the epidemics incidence decreases.
2,500-year Evolution of the Term Epidemic
Martin-Granel, Estelle
2006-01-01
The term epidemic (from the Greek epi [on] plus demos [people]), first used by Homer, took its medical meaning when Hippocrates used it as the title of one of his famous treatises. At that time, epidemic was the name given to a collection of clinical syndromes, such as coughs or diarrheas, occurring and propagating in a given period at a given location. Over centuries, the form and meaning of the term have changed. Successive epidemics of plague in the Middle Ages contributed to the definition of an epidemic as the propagation of a single, well-defined disease. The meaning of the term continued to evolve in the 19th-century era of microbiology. Its most recent semantic evolution dates from the last quarter of the 20th century, and this evolution is likely to continue in the future. PMID:16707055
Epidemic spreading on interconnected networks.
Saumell-Mendiola, Anna; Serrano, M Ángeles; Boguñá, Marián
2012-08-01
Many real networks are not isolated from each other but form networks of networks, often interrelated in nontrivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop a heterogeneous mean-field approach that allows us to calculate the conditions for the emergence of an endemic state. Interestingly, a global endemic state may arise in the coupled system even though the epidemics is not able to propagate on each network separately and even when the number of coupling connections is small. Our analytic results are successfully confronted against large-scale numerical simulations.
Epidemic dynamics on a risk-based evolving social network
Antwi, Shadrack; Shaw, Leah
2013-03-01
Social network models have been used to study how behavior affects the dynamics of an infection in a population. Motivated by HIV, we consider how a trade-off between benefits and risks of sexual connections determine network structure and disease prevalence. We define a stochastic network model with formation and breaking of links as changes in sexual contacts. Each node has an intrinsic benefit its neighbors derive from connecting to it. Nodes' infection status is not apparent to others, but nodes with more connections (higher degree) are assumed more likely to be infected. The probability to form and break links is determined by a payoff computed from the benefit and degree-dependent risk. The disease is represented by a SI (susceptible-infected) model. We study network and epidemic evolution via Monte Carlo simulation and analytically predict the behavior with a heterogeneous mean field approach. The dependence of network connectivity and infection threshold on parameters is determined, and steady state degree distribution and epidemic levels are obtained. We also study a situation where system-wide infection levels alter perception of risk and cause nodes to adjust their behavior. This is a case of an adaptive network, where node status feeds back to change network geometry.
Coevolution of Epidemics, Social Networks, and Individual Behavior: A Case Study
Chen, Jiangzhuo; Marathe, Achla; Marathe, Madhav
This research shows how a limited supply of antivirals can be distributed optimally between the hospitals and the market so that the attack rate is minimized and enough revenue is generated to recover the cost of the antivirals. Results using an individual based model find that prevalence elastic demand behavior delays the epidemic and change in the social contact network induced by isolation reduces the peak of the epidemic significantly. A microeconomic analysis methodology combining behavioral economics and agent-based simulation is a major contribution of this work. In this paper we apply this methodology to analyze the fairness of the stockpile distribution, and the response of human behavior to disease prevalence level and its interaction with the market.
HIV epidemics and prevention responses in Asia and Eastern Europe: lessons to be learned?
DEFF Research Database (Denmark)
Bridge, Jamie; Lazarus, Jeff; Atun, Rifat
2010-01-01
This paper describes characteristics of the HIV epidemics in Eastern Europe and Central Asia (EECA) and Asia and Central Asia, and draws comparisons between these regions. It focuses on the role that key populations continue to play in HIV transmission in both regions, the challenges that this po...
Hybrid epidemic spreading - from Internet worms to HIV infection
Zhang, C.
2015-01-01
Epidemic phenomena are ubiquitous, ranging from infectious diseases, computer viruses, to information dissemination. Epidemics have traditionally been studied as a single spreading process, either in a fully mixed population or on a network. Many epidemics, however, are hybrid, employing more than one spreading mechanism. For example, the Internet worm Conficker spreads locally targeting neighbouring computers in local networks as well as globally by randomly probing any computer on the Inter...
Milleliri, J M; Soares, J L; Signoret, J; Bechen, R; Lamarque, D; Boutin, J P; Coué, J C; Niel, L; Merouze, F; Rey, J L
1995-09-01
The authors describe the extension of an outbreak of bacillary dysentery among the Rwandese populations seeking refuge in the region of Goma, Zaire in august 1994. Analysis of the epidemiological surveillance data and of the bacteriological laboratory results of the Bioforce, show that this epidemic was probably facilitated by the preceding cholera outbreak. In such circumstances, rapid sterilization of the virus reservoir, by short course treatments, might be beneficial in limiting the extension of the epidemic.
Characterization and Proposed Nomenclature of Epidemic Strains of MRSA in Canada
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AE Simor
1999-01-01
Full Text Available The incidence of methicillin-resistant Staphylococcus aureus (MRSA has been increasing in many Canadian hospitals over the past few years. Some strains may be considered ‘epidemic’, in that they are clinically or epidemiologically significant, and have been identified in patients from multiple hospitals and geographic regions across the country. This paper describes phenotypic and genotypic characteristics of four epidemic MRSA strains in Canada and proposes standardized nomenclature.
Directory of Open Access Journals (Sweden)
Stéfan Tzortzis
2012-01-01
Full Text Available At the beginning of the 18th century, the Provence region was hit by several severe epidemics whose causes are still not clearly understood.To draw up epidemic profiles and to identify the pathogenic agents concerned, we constituted a large onomastic database and built ageographic information system for Martigues, a medium-sized community in the south of France. The cross-linking of epidemiological,spatial and demographical data allows us to propose a new diagnosis for the epidemic which reached Martigues in the autumn of 1705.