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## A vaccination game based on public health actions and personal decisions

SCHIMIT, P. H. T.; MONTEIRO, L. H. A.
Fonte: ELSEVIER SCIENCE BV Publicador: ELSEVIER SCIENCE BV
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
46.07%
Susceptible-infective-removed (SIR) models are commonly used for representing the spread of contagious diseases. A SIR model can be described in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. Here, this framework is employed for investigating the consequences of applying vaccine against the propagation of a contagious infection, by considering vaccination as a game, in the sense of game theory. In this game, the players are the government and the susceptible newborns. In order to maximize their own payoffs, the government attempts to reduce the costs for combating the epidemic, and the newborns may be vaccinated only when infective individuals are found in their neighborhoods and/or the government promotes an immunization program. As a consequence of these strategies supported by cost-benefit analysis and perceived risk, numerical simulations show that the disease is not fully eliminated and the government implements quasi-periodic vaccination campaigns. (C) 2011 Elsevier B.V. All rights reserved.; CNPq

## Simulando o processo epidêmico da rubéola via autômatos celulares em diferentes topologias : a dependência da idade no fator infecção

Correa, Fabio Arreguy Camargo
Tipo: Trabalho de Conclusão de Curso Formato: application/pdf
POR
Relevância na Pesquisa
46.09%
Este trabalho apresenta um modelo epidêmico baseado em autômato celular que descreve a propagação da rubéola, baseando-se no modelo inicialmente proposto por (AMAKU et al., 2003),introduzindo dependência da idade dos indivíduos em um modelo canônico de propagação epidêmica, conhecido como modelo SIR. É analisada a evolução da epidemia ao longo do tempo em diferentes topologias de redes complexas. Os cenários escolhidos visam caracterizar parâmetros importantes e condições que exerçam influência significativa na dinâmica da epidemia em questão.; This paper presents an epidemic model based on cellular automata, which describes the spread of rubella, introducing age dependence of individuals in a canonical model of epidemic spread, known as SIR model . It analyzes the time-evolving of the epidemic process in different topologies of complex networks. The scenarios are chosen in order to characterize importants parameters and conditions which affect significantly the dynamics of the epidemic in question.

## Teoremas limiares para o modelo SIR estocástico de epidemia; Threshold theorems for the SIR stochastic epidemic model

Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
46.28%
Este trabalho tem como objetivo estudar o modelo SIR (suscetível-infectado-removido) de epidemia nas versões determinística e estocástica. Nosso objetivo é encontrar limitantes para a probabilidade de que o tamanho da epidemia não sobrepasse certa proporção do número inicial de suscetíveis. Iniciamos apresentando as definições e a dinâmica do processo de epidemia determinístico. Obtemos um valor limiar para o número inicial de suscetíveis para que a epidemia exploda ou não. Consideramos o modelo de epidemia estocástico SIR assumindo que não há período latente, isto é, que um infectado pode transmitir a infecção ao instante de ser contagiado. O modelo é considerado com uma configuração inicial de suscetíveis e infectados e é feita especial ênfases no estudo da variável aleatória 'tamanho da epidemia', que é definida como a diferença entre o número de suscetíveis ao começar e ao terminar a propagação da doença. Como na parte determinística, obtemos teoremas limiares para o modelo de epidemia estocástico. Os métodos usados para encontrar os limitantes são os de análise da cadeia de Markov imersa e de comparação estocástica.; This work has as objective to study the SIR (susceptible-infected-removed) epidemic model in the deterministic and stochastic version. Our objective is to find bounds for the probability that the size of the epidemic does not exceed certain proportion of the initial number of susceptible individuals. We begin presenting the definitions and the dynamics for the deterministic model for a general epidemic. We obtain a threshold value for the initial number of susceptible individuals for the epidemic to build up or not. As fundamental part of this work...

## An application of the SIR model to the evolution of epidemics in Portugal

Correia, António M.; Mena, Filipe C.; Soares, A. J.
Tipo: Conferência ou Objeto de Conferência
Relevância na Pesquisa
45.94%
We apply the SIR model to study the evolution of Measles and Hepatitis C in Portugal using data from 1996 until 2007. Our results are potentially interesting to forecast the evolution of those viruses in subsequent years.

## Analysis and fitting of an SIR model with host response to infection load for a plant disease

Gilligan, C. A.; Gubbins, S.; Simons, S. A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.12%
We reformulate a model for botanical epidemics into an SIR form for susceptible (S), infected (I) and removed (R) plant organs, in order to examine the effects of different models for the effect of host responses to the load of infection on the production of susceptible tissue. The new formulation also allows for a decline in host susceptibility with age. The model is analysed and tested for the stem canker disease of potatoes, caused by the soil-borne fungus, Rhizoctonia solani. Using a combination of model fitting to field data and analysis of model behaviour, we show that a function for host response to the amount (load) of parasite infection is critical in the description of the temporal dynamics of susceptible and infected stems in epidemics of R. solani. Several different types of host response to infection are compared including two that allow for stimulation of the plant to produce more susceptible tissue at low levels of disease and inhibition at higher levels. We show that when the force of infection decays with time, due to increasing resistance of the host, the equilibrium density of susceptible stems depends on the parameters and initial conditions. The models differ in sensitivity to small changes in disease transmission with some showing marked qualitative changes leading to a flush of susceptible stems at low levels of disease transmission. We conclude that there is no evidence to reject an SIR model with a simpler linear term for the effect of infection load on the production of healthy tissue...

## Combined effects of prevention and quarantine on a breakout in SIR model

Kato, Fuminori; Tainaka, Kei-ichi; Sone, Shogo; Morita, Satoru; Iida, Hiroyuki; Yoshimura, Jin
Fonte: Nature Publishing Group Publicador: Nature Publishing Group
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.97%
Recent breakouts of several epidemics, such as flu pandemics, are serious threats to human health. The measures of protection against these epidemics are urgent issues in epidemiological studies. Prevention and quarantine are two major approaches against disease spreads. We here investigate the combined effects of these two measures of protection using the SIR model. We use site percolation for prevention and bond percolation for quarantine applying on a lattice model. We find a strong synergistic effect of prevention and quarantine under local interactions. A slight increase in protection measures is extremely effective in the initial disease spreads. Combination of the two measures is more effective than a single protection measure. Our results suggest that the protection policy against epidemics should account for both prevention and quarantine measures simultaneously.

## Synchrony of Sylvatic Dengue Isolations: A Multi-Host, Multi-Vector SIR Model of Dengue Virus Transmission in Senegal

Althouse, Benjamin M.; Lessler, Justin; Sall, Amadou A.; Diallo, Mawlouth; Hanley, Kathryn A.; Watts, Douglas M.; Weaver, Scott C.; Cummings, Derek A. T.
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.94%
Isolations of sylvatic dengue-2 virus from mosquitoes, humans and non-human primates in Senegal show synchronized multi-annual dynamics over the past 50 years. Host demography has been shown to directly affect the period between epidemics in other pathogen systems, therefore, one might expect unsynchronized multi-annual cycles occurring in hosts with dramatically different birth rates and life spans. However, in Senegal, we observe a single synchronized eight-year cycle across all vector species, suggesting synchronized dynamics in all vertebrate hosts. In the current study, we aim to explore two specific hypotheses: 1) primates with different demographics will experience outbreaks of dengue at different periodicities when observed as isolated systems, and that coupling of these subsystems through mosquito biting will act to synchronize incidence; and 2) the eight-year periodicity of isolations observed across multiple primate species is the result of long-term cycling in population immunity in the host populations. To test these hypotheses, we develop a multi-host, multi-vector Susceptible, Infected, Removed (SIR) model to explore the effects of coupling multiple host-vector systems of dengue virus transmission through cross-species biting rates. We find that under small amounts of coupling...

## Modelos de ecuaciones diferenciales para la propagación de enfermedades infecciosas; Models of differential equations for the spread of infectious diseases

García Piñera, Andrea
Tipo: Trabalho de Conclusão de Curso
SPA
Relevância na Pesquisa
46.1%
RESUMEN: El estudio de las epidemias siempre ha despertado gran interés, tanto en el pasado como en la actualidad. La historia de la humanidad está marcada por grandes epidemias como la Peste Negra o la viruela que acabaron con la vida de más de 300 millones de personas. En los últimos dos años, la epidemia del ébola está despertando mucho interés debido a su gran letalidad y a ser la causante de más de 5600 muertes en el continente africano. La modelización matemática es una herramienta que cada vez se utiliza más en epidemiología. A lo largo del presente trabajo estudiaremos el modelo SIR, introducido en 1927 por Kermack y McKendrick, y sus variantes más conocidas para predecir la propagación de enfermedades infecciosas en una población, tanto desde el punto de vista teórico como computacional.; ABSTRACT: The study of epidemics has always generated a great deal of interest, from earlier times as well as the present. Mankind history is marked by major epidemics such as the Black Death or smallpox that killed more than 300 million people. In the last two years, the ebola epidemic is attracting a lot of interest because of its high lethality and for being the cause of over 5,600 deaths in Africa. Mathematical modelling is a widely used tool in epidemiology. In this work we study SIR model...

## Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth–death SIR model

Kühnert, Denise; Stadler, Tanja; Vaughan, Timothy G.; Drummond, Alexei J.
Fonte: The Royal Society Publicador: The Royal Society
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.04%
The evolution of RNA viruses, such as human immunodeficiency virus (HIV), hepatitis C virus and influenza virus, occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible–infected–removed (SIR) model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our birth–death SIR method to two viral datasets. First, five HIV type 1 clusters sampled in the UK between 1999 and 2003 are analysed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 1990s. The analysis of a hepatitis C virus genotype 2c dataset shows that the local epidemic in the Córdoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880 to 1920. The estimated time of epidemic peak is around 1970.

## Information Source Detection in the SIR Model: A Sample Path Based Approach

Zhu, Kai; Ying, Lei
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.94%
This paper studies the problem of detecting the information source in a network in which the spread of information follows the popular Susceptible-Infected-Recovered (SIR) model. We assume all nodes in the network are in the susceptible state initially except the information source which is in the infected state. Susceptible nodes may then be infected by infected nodes, and infected nodes may recover and will not be infected again after recovery. Given a snapshot of the network, from which we know all infected nodes but cannot distinguish susceptible nodes and recovered nodes, the problem is to find the information source based on the snapshot and the network topology. We develop a sample path based approach where the estimator of the information source is chosen to be the root node associated with the sample path that most likely leads to the observed snapshot. We prove for infinite-trees, the estimator is a node that minimizes the maximum distance to the infected nodes. A reverse-infection algorithm is proposed to find such an estimator in general graphs. We prove that for $g$-regular trees such that $gq>1,$ where $g$ is the node degree and $q$ is the infection probability, the estimator is within a constant distance from the actual source with a high probability...

## A study of the influence of the mobility on the phase transitions of the synchronous SIR model

da Silva, Roberto; Fernandes, Henrique A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.94%
By using an appropriate version of the synchronous SIR model, we studied the effects of dilution and mobility on the critical immunization rate. We showed that, by applying time-dependent Monte Carlo (MC) simulations at criticality, and taking into account the optimization of the power law for the density of infected individuals, the critical immunization necessary to block the epidemic in two-dimensional lattices decreases as dilution increases with a logarithmic dependence. On the other hand, the mobility minimizes such effects and the critical immunizations is greater when the probability of movement of the individuals increases.; Comment: 8 pages, 4 figures, 1 table

## SIR model on a dynamical network and the endemic state of an infectious disease

Dottori, Martin; Fabricius, Gabriel
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.11%
In this work we performed a numerical study of an epidemic model that mimics the endemic state of whooping cough in the pre-vaccine era. We considered a stochastic SIR model on dynamical networks that involve local and global contacts among individuals and analyzed the influence of the network properties on the characterization of the quasi-stationary state. We computed probability density functions (PDF) for infected fraction of individuals and found that they are well fitted by gamma functions, excepted the tails of the distributions that are q-exponentials. We also computed the fluctuation power spectra of infective time series for different networks. We found that network effects can be partially absorbed by rescaling the rate of infective contacts of the model. An explicit relation between the effective transmission rate of the disease and the correlation of susceptible individuals with their infective nearest neighbours was obtained. This relation quantifies the known screening of infective individuals observed in these networks. We finally discuss the goodness and limitations of the SIR model with homogeneous mixing and parameters taken from epidemiological data to describe the dynamic behaviour observed in the networks studied.

## Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates

Harko, Tiberiu; Lobo, Francisco S. N.; Mak, M. K.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.25%
In this paper, the exact analytical solution of the Susceptible-Infected-Recovered (SIR) epidemic model is obtained in a parametric form. By using the exact solution we investigate some explicit models corresponding to fixed values of the parameters, and show that the numerical solution reproduces exactly the analytical solution. We also show that the generalization of the SIR model, including births and deaths, described by a nonlinear system of differential equations, can be reduced to an Abel type equation. The reduction of the complex SIR model with vital dynamics to an Abel type equation can greatly simplify the analysis of its properties. The general solution of the Abel equation is obtained by using a perturbative approach, in a power series form, and it is shown that the general solution of the SIR model with vital dynamics can be represented in an exact parametric form.; Comment: 13 pages, 4 figures, accepted for publication in Applied Mathematics and Computation

## Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth-death SIR model

Kühnert, Denise; Stadler, Tanja; Vaughan, Timothy G.; Drummond, Alexei J.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.04%
The evolution of RNA viruses such as HIV, Hepatitis C and Influenza virus occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible-infected-removed (SIR) model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our Birth-Death SIR method (BDSIR) to two viral data sets. First, five human immunodeficiency virus type 1 clusters sampled in the United Kingdom between 1999 and 2003 are analyzed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 90's. The analysis of a hepatitis C virus (HCV) genotype 2c data set shows that the local epidemic in the C\'ordoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880--1920. The estimated time of epidemic peak is around 1970.; Comment: Journal link: http://rsif.royalsocietypublishing.org/content/11/94/20131106.full

## Exact solution of a stochastic SIR model

Schütz, Gunter M.; Brandau, Marian; Trimper, Steffen
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.17%
The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an infectious $I$- type provided that both are in contact. The $I$- type may recover with a rate $\gamma$ and from then on stay immune. Due to the coupling between the different individuals, the model is nonlinear and out of equilibrium. We adopt a stochastic individual-based description where individuals are represented by nodes of a graph and contact is defined by the links of the graph. Mapping the underlying Master equation into a quantum formulation in terms of spin operators, the hierarchy of evolution equations can be solved exactly for arbitrary initial conditions on a linear chain. In case of uncorrelated random initial conditions the exact time evolution for all three individuals of the SIR model is given analytically. Depending on the initial conditions and reaction rates $\beta$ and $\gamma$, the $I$-population may increase initially before decaying to zero. Due to fluctuations, isolated regions of susceptible individuals evolve and unlike in the standard mean-field SIR model one observes a finite stationary distribution of the $S$-type even for large population size. The exact results for the ensemble averaged population size are compared with simulations for single realizations of the process and also with standard mean field theory which is expected to be valid on large fully-connected graphs.; Comment: 19 pages...

## A fractional order recovery SIR model from a stochastic process

Angstmann, C. N.; Henry, B. I.; McGann, A. V.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.19%
Over the past several decades there has been a proliferation of epidemiological models with ordinary derivatives replaced by fractional derivatives in an an-hoc manner. These models may be mathematically interesting but their relevance is uncertain. Here we develop an SIR model for an epidemic, including vital dynamics, from an underlying stochastic process. We show how fractional differential operators arise naturally in these models whenever the recovery time from the disease is power law distributed. This can provide a model for a chronic disease process where individuals who are infected for a long time are unlikely to recover. The fractional order recovery model is shown to be consistent with the Kermack-McKendrick age-structured SIR model and it reduces to the Hethcote-Tudor integral equation SIR model. The derivation from a stochastic process is extended to discrete time, providing a stable numerical method for solving the model equations. We have carried out simulations of the fractional order recovery model showing convergence to equilibrium states. The number of infecteds in the endemic equilibrium state increases as the fractional order of the derivative tends to zero.; Comment: 32 pages, 3 figures

## A Fractional-Order Infectivity SIR Model

Angstmann, Christopher N; Henry, Bruce I; McGann, Anna V
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.28%
Fractional-order SIR models have become increasingly popular in the literature in recent years, however unlike the standard SIR model, they often lack a derivation from an underlying stochastic process. Here we derive a fractional-order infectivity SIR model from a stochastic process that incorporates a time-since-infection dependence on the infectivity of individuals. The fractional derivative appears in the generalised master equations of a continuous time random walk through SIR compartments, with a power-law function in the infectivity. We show that this model can also be formulated as an infection-age structured Kermack-McKendrick integro-differential SIR model. Under the appropriate limit the fractional infectivity model reduces to the standard ordinary differential equation SIR model.; Comment: 16 pages, no figures

## Variance in System Dynamics and Agent Based Modelling Using the SIR Model of Infectious Disease

Ahmed, Aslam; Greensmith, Julie; Aickelin, Uwe
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.15%
Classical deterministic simulations of epidemiological processes, such as those based on System Dynamics, produce a single result based on a fixed set of input parameters with no variance between simulations. Input parameters are subsequently modified on these simulations using Monte-Carlo methods, to understand how changes in the input parameters affect the spread of results for the simulation. Agent Based simulations are able to produce different output results on each run based on knowledge of the local interactions of the underlying agents and without making any changes to the input parameters. In this paper we compare the influence and effect of variation within these two distinct simulation paradigms and show that the Agent Based simulation of the epidemiological SIR (Susceptible, Infectious, and Recovered) model is more effective at capturing the natural variation within SIR compared to an equivalent model using System Dynamics with Monte-Carlo simulation. To demonstrate this effect, the SIR model is implemented using both System Dynamics (with Monte-Carlo simulation) and Agent Based Modelling based on previously published empirical data.; Comment: Proceedings of the 26th European Conference on Modelling and Simulation (ECMS)...

## On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice

Tomé, Tânia; Ziff, Robert M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.97%
By means of numerical simulations and epidemic analysis, the transition point of the stochastic, asynchronous Susceptible-Infected-Recovered (SIR) model on a square lattice is found to be c_0=0.1765005(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda_c = (1-c_0)/c_0 = 4.66571(3) and a net transmissibility of (1-c_0)/(1 + 3 c_0) = 0.538410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the 2-d percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.; Comment: 9 pages, 5 figures. Accepted for publication, Physical Review E

## SIR model with local and global infective contacts: A deterministic approach and applications

Maltz, Alberto; Fabricius, Gabriel