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## Susceptible-infected-recovered and susceptible-exposed-infected models

Fonte: IOP PUBLISHING LTD
Publicador: IOP PUBLISHING LTD

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

46%

#MOLECULAR-SIZE DISTRIBUTION#CRITICAL-BEHAVIOR#EPIDEMIC PROCESS#PERCOLATION#LATTICE#IMMUNIZATION#THRESHOLD#POLYMERS#GELATION#SPREAD#Physics, Multidisciplinary

Two stochastic epidemic lattice models, the susceptible-infected-recovered and the susceptible-exposed-infected models, are studied on a Cayley tree of coordination number k. The spreading of the disease in the former is found to occur when the infection probability b is larger than b(c) = k/2(k - 1). In the latter, which is equivalent to a dynamic site percolation model, the spreading occurs when the infection probability p is greater than p(c) = 1/(k - 1). We set up and solve the time evolution equations for both models and determine the final and time-dependent properties, including the epidemic curve. We show that the two models are closely related by revealing that their relevant properties are exactly mapped into each other when p = b/[k - (k - 1) b]. These include the cluster size distribution and the density of individuals of each type, quantities that have been determined in closed forms.; Brazilian agency CNPq; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); INCT/CNPq of Complex Fluids; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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## Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

Fonte: ELSEVIER SCIENCE BV
Publicador: ELSEVIER SCIENCE BV

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

46.2%

#Population dynamics#Epidemic models#SIRS models#PREY CELLULAR-AUTOMATON#CRITICAL-BEHAVIOR#SPATIAL STRUCTURE#PREDATOR#OSCILLATIONS#COEXISTENCE#Physics, Multidisciplinary

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S -> I -> R -> S (SIRS). The open process S -> I -> R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations. (C) 2009 Elsevier B.V. All rights reserved.; Brazilian agency CNPq; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); INCT of Complex Fluids (CNPq and FAPESP); Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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## Modelagem de problemas da dinâmica de populações por meio da dinâmica estocástica; Modeling problems of population by the stochastic dynamics

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 29/09/2009
PT

Relevância na Pesquisa

46.03%

#Dinâmica de populações#Epidemic models#Física#Modelos epidemiológicos#Mudança de fase#Phase transition#Physics#Population dynamics#Processo estotástico#Stochastic process

Apresentamos o estudo de três modelos estocásticos governadas por equações mestras que descrevem a propagação de epidemias em uma comunidade de indivíduos;; We present a study of three stochastic models, governed by master equations, that decribe the epidemic spreding in a community of individuals;

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## 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

Publicado em 25/02/2015
PT

Relevância na Pesquisa

66.21%

#Processo estocástico#Markov#Cadeias de#Probabilidades#Modelos epidemiológicos SIR#Stochastic processes#Markov chains#Probabilities#SIR epidemic models

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...

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## Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

EN

Relevância na Pesquisa

46.33%

In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic SIR epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR models with random and proportionate mixing. The epidemic percolation networks for these models are purely directed because undirected edges disappear in the limit of a large population. In a series of simulations, we show that epidemic percolation networks accurately predict the mean outbreak size and probability and final size of an epidemic for a variety of epidemic models in homogeneous and heterogeneous populations. Finally, we show that epidemic percolation networks can be used to re-derive classical results from several different areas of infectious disease epidemiology. In an appendix, we show that an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model in a closed population and prove that the distribution of outbreak sizes given the infection of any given node in the SIR model is identical to the distribution of its out-component sizes in the corresponding probability space of epidemic percolation networks. We conclude that the theory of percolation on semi-directed networks provides a very general framework for the analysis of stochastic SIR models in closed populations.

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## Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

EN

Relevância na Pesquisa

45.98%

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.

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## Improved Estimation of the Initial Number of Susceptible Individuals in the General Stochastic Epidemic Model Using Penalized Likelihood

Fonte: Hindawi Publishing Corporation
Publicador: Hindawi Publishing Corporation

Tipo: Artigo de Revista Científica

EN

Relevância na Pesquisa

46.01%

The initial size of a completely susceptible population in a group of individuals plays a key role in drawing inferences for epidemic models. However, this can be difficult to obtain in practice because, in any population, there might be individuals who may not transmit the disease during the epidemic. This short note describes how to improve the maximum likelihood estimators of the infection rate and the initial number of susceptible individuals and provides their approximate Hessian matrix for the general stochastic epidemic model by using the concept of the penalized likelihood function. The simulations of major epidemics show significant improvements in performance in averages and coverage ratios for the suggested estimator of the initial number in comparison to existing methods. We applied the proposed method to the Abakaliki smallpox data.

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## Bayesian spatio-temporal epidemic models with applications to sheep pox

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/03/2014

Relevância na Pesquisa

46%

Epidemic data often possess certain characteristics, such as the presence of
many zeros, the spatial nature of the disease spread mechanism or environmental
noise. This paper addresses these issues via suitable Bayesian modelling. In
doing so we utilise stochastic regression models appropriate for
spatio-temporal count data with an excess number of zeros. The developed
regression framework can incorporate serial correlation and time varying
covariates through an Ornstein Uhlenbeck process formulation. In addition, we
explore the effect of different priors, including default options and
techniques based upon variations of mixtures of $g$-priors. The effect of
different distance kernels for the epidemic model component is investigated. We
proceed by developing branching process-based methods for testing scenarios for
disease control, thus linking traditional spatio-temporal models with epidemic
processes, useful in policy-focused decision making. The approach is
illustrated with an application to a sheep pox dataset from the Evros region,
Greece.

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## Statistical inference for stochastic epidemic models with three levels of mixing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/08/2009

Relevância na Pesquisa

55.98%

A stochastic epidemic model is defined in which each individual belongs to a
household, a secondary grouping (typically school or workplace) and also the
community as a whole. Moreover, infectious contacts take place in these three
settings according to potentially different rates. For this model we consider
how different kinds of data can be used to estimate the infection rate
parameters with a view to understanding what can and cannot be inferred, and
with what precision. Among other things we find that temporal data can be of
considerable inferential benefit compared to final size data, that the degree
of heterogeneity in the data can have a considerable effect on inference for
non-household transmission, and that inferences can be materially different
from those obtained from a model with two levels of mixing.
Keywords: Basic reproduction number, Bayesian inference, Epidemic model,
Infectious disease data, Markov chain Monte Carlo, Networks.

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## Sequential Bayesian Inference in Hidden Markov Stochastic Kinetic Models with Application to Detection and Response to Seasonal Epidemics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/01/2013

Relevância na Pesquisa

46.01%

We study sequential Bayesian inference in stochastic kinetic models with
latent factors. Assuming continuous observation of all the reactions, our focus
is on joint inference of the unknown reaction rates and the dynamic latent
states, modeled as a hidden Markov factor. Using insights from nonlinear
filtering of continuous-time jump Markov processes we develop a novel
sequential Monte Carlo algorithm for this purpose. Our approach applies the
ideas of particle learning to minimize particle degeneracy and exploit the
analytical jump Markov structure. A motivating application of our methods is
modeling of seasonal infectious disease outbreaks represented through a
compartmental epidemic model. We demonstrate inference in such models with
several numerical illustrations and also discuss predictive analysis of
epidemic countermeasures using sequential Bayes estimates.; Comment: 26 pages, 7 figures

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## Dynamical Monte Carlo method for stochastic epidemic models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

46%

In this work we introduce a new approach to Dynamical Monte Carlo methods to
simulate markovian processes. We apply this approach to formulate and study an
epidemic generalized SIRS model. The results are in excellent agreement with
the fourth order Runge-Kutta method in a region of deterministic solution.
Introducing local stochastic interactions, the Runge-Kutta method is no longer
applicable. Thus, we solve the system described by a set of stochastic
differential equations by a Dynamical Monte Carlo technique and check the
solutions self-consistently with a stochastic version of the Euler method. We
also analyzed the results under the herd-immunity concept.; Comment: 18 pages, 4 figures in ps format, regular article, Latex, written
with Scientific WorkPlace 3.51

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## A note on fractional linear pure birth and pure death processes in epidemic models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/08/2011

Relevância na Pesquisa

46.03%

In this note we highlight the role of fractional linear birth and linear
death processes recently studied in \citet{sakhno} and \citet{pol}, in relation
to epidemic models with empirical power law distribution of the events. Taking
inspiration from a formal analogy between the equation of self consistency of
the epidemic type aftershock sequences (ETAS) model, and the fractional
differential equation describing the mean value of fractional linear growth
processes, we show some interesting applications of fractional modelling to
study \textit{ab initio} epidemic processes without the assumption of any
empirical distribution. We also show that, in the frame of fractional
modelling, subcritical regimes can be linked to linear fractional death
processes and supercritical regimes to linear fractional birth processes.
Moreover we discuss a simple toy model to underline the possible application of
these stochastic growth models to more general epidemic phenomena such as
tumoral growth.

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## Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

46.33%

#Quantitative Biology - Quantitative Methods#Condensed Matter - Statistical Mechanics#Mathematics - Probability

In this paper, we outline the theory of epidemic percolation networks and
their use in the analysis of stochastic SIR epidemic models on undirected
contact networks. We then show how the same theory can be used to analyze
stochastic SIR models with random and proportionate mixing. The epidemic
percolation networks for these models are purely directed because undirected
edges disappear in the limit of a large population. In a series of simulations,
we show that epidemic percolation networks accurately predict the mean outbreak
size and probability and final size of an epidemic for a variety of epidemic
models in homogeneous and heterogeneous populations. Finally, we show that
epidemic percolation networks can be used to re-derive classical results from
several different areas of infectious disease epidemiology. In an appendix, we
show that an epidemic percolation network can be defined for any
time-homogeneous stochastic SIR model in a closed population and prove that the
distribution of outbreak sizes given the infection of any given node in the SIR
model is identical to the distribution of its out-component sizes in the
corresponding probability space of epidemic percolation networks. We conclude
that the theory of percolation on semi-directed networks provides a very
general framework for the analysis of stochastic SIR models in closed
populations.; Comment: 40 pages...

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## Stochastic epidemic models featuring contact tracing with delays

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/12/2015

Relevância na Pesquisa

46.04%

This paper is concerned with a stochastic model for the spread of an SEIR
(susceptible -> exposed (=latent) -> infective -> removed) epidemic with a
contact tracing scheme, in which removed individuals may name some of their
infectious contacts, who are then removed if they have not been already after
some tracing delay. The epidemic is analysed via an approximating, modified
birth-death process, for which a type-reproduction number is derived in terms
of unnamed individuals, that is shown to be infinite when the contact rate is
sufficiently large. We obtain explicit results under the assumption of either
constant or exponentially distributed infectious periods, including the
epidemic extinction probability in the former case. Numerical illustrations
show that, while the distributions of latent periods and delays have an effect
on the spread of the epidemic, the assumption of whether the delays experienced
by individuals infected by the same individual are of the same or independent
length makes little difference.; Comment: Mathematical Biosciences 2015

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## Second Quantization Approach to Stochastic Epidemic Models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/09/2015

Relevância na Pesquisa

66.08%

We show how the standard field theoretical language based on creation and
annihilation operators may be used for a straightforward derivation of closed
master equations describing the population dynamics of multivariate stochastic
epidemic models. In order to do that, we introduce an SIR-inspired stochastic
model for hepatitis C virus epidemic, from which we obtain the time evolution
of the mean number of susceptible, infected, recovered and chronically infected
individuals in a population whose total size is allowed to change.; Comment: To appear in Biomedical Sciences Today, 6 pages

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## Critical scaling of stochastic epidemic models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/09/2007

Relevância na Pesquisa

55.99%

In the simple mean-field SIS and SIR epidemic models, infection is
transmitted from infectious to susceptible members of a finite population by
independent $p-$coin tosses. Spatial variants of these models are proposed, in
which finite populations of size $N$ are situated at the sites of a lattice and
infectious contacts are limited to individuals at neighboring sites. Scaling
laws for both the mean-field and spatial models are given when the infection
parameter $p$ is such that the epidemics are critical. It is shown that in all
cases there is a critical threshold for the numbers initially infected: below
the threshold, the epidemic evolves in essentially the same manner as its
branching envelope, but at the threshold evolves like a branching process with
a size-dependent drift.; Comment: Published at http://dx.doi.org/10.1214/074921707000000346 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## Information geometry and entropy in a stochastic epidemic rate process

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

46.04%

#Quantitative Biology - Populations and Evolution#Quantitative Biology - Quantitative Methods#92B05, 92C60, 65C50

Epidemic models with inhomogeneous populations have been used to study major
outbreaks and recently Britton and Lindenstrand \cite{BL} described the case
when latency and infectivity have independent gamma distributions. They found
that variability in these random variables had opposite effects on the epidemic
growth rate. That rate increased with greater variability in latency but
decreased with greater variability in infectivity. Here we extend their result
by using the McKay bivariate gamma distribution for the joint distribution of
latency and infectivity, recovering the above effects of variability but
allowing possible correlation. We use methods of stochastic rate processes to
obtain explicit solutions for the growth of the epidemic and the evolution of
the inhomogeneity and information entropy. We obtain a closed analytic solution
to the evolution of the distribution of the number of uninfected individuals as
the epidemic proceeds, and a concomitant expression for the decay of entropy.
The family of McKay bivariate gamma distributions has a tractable information
geometry which provides a framework in which the evolution of distributions can
be studied as the outbreak grows, with a natural distance structure for
quantitative tracking of progress.; Comment: 10 pages...

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## Stochastic epidemic models: a survey

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/10/2009

Relevância na Pesquisa

66.15%

#Mathematics - Probability#Mathematics - Statistics Theory#Statistics - Applications#Statistics - Methodology

This paper is a survey paper on stochastic epidemic models. A simple
stochastic epidemic model is defined and exact and asymptotic model properties
(relying on a large community) are presented. The purpose of modelling is
illustrated by studying effects of vaccination and also in terms of inference
procedures for important parameters, such as the basic reproduction number and
the critical vaccination coverage. Several generalizations towards realism,
e.g. multitype and household epidemic models, are also presented, as is a model
for endemic diseases.; Comment: 26 pages, 4 figures

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## On the advancement of optimal experimental design with applications to infectious diseases.

Fonte: Universidade de Adelaide
Publicador: Universidade de Adelaide

Tipo: Tese de Doutorado

Publicado em //2015

Relevância na Pesquisa

56.11%

In this thesis, we investigate the optimal experimental design of some common biological experiments. The theory of optimal experimental design is a statistical tool that allows us to determine the optimal experimental protocol to gain the most information about a particular process, given constraints on resources. We focus on determining the optimal design for experiments where the underlying model is a Markov chain | a particularly useful stochastic model. Markov chains are commonly used to represent a range of biological systems, for example: the evolution and spread of populations and disease, competition between species, and evolutionary genetics. There has been little research into the optimal experimental design of systems where the underlying process is modelled as a Markov chain, which is surprising given their suitability for representing the random behaviour of many natural processes. While the first paper to consider the optimal experimental design of a system where the underlying process was modelled as a Markov chain was published in the mid 1980's, this research area has only recently started to receive significant attention. Current methods of evaluating the optimal experimental design within a Bayesian framework can be computationally inefficient...

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## Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods

Fonte: Blackwell Publishing Ltd
Publicador: Blackwell Publishing Ltd

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

66.03%

#Keywords: Bayesian statistics#Epidemic data#Gibbs sampler#Likelihood approximation#Markov chain Monte Carlo methods#Metropolis-hastings algorithm#Missing data#Stochastic epidemic models

The analysis of infectious disease data presents challenges arising from the dependence in the data and the fact that only part of the transmission process is observable. These difficulties are usually overcome by making simplifying assumptions. The paper explores the use of Markov chain Monte Carlo (MCMC) methods for the analysis of infectious disease data, with the hope that they will permit analyses to be made under more realistic assumptions. Two important kinds of data sets are considered, containing temporal and non-temporal information, from outbreaks of measles and influenza. Stochastic epidemic models are used to describe the processes that generate the data. MCMC methods are then employed to perform inference in a Bayesian context for the model parameters. The MCMC methods used include standard algorithms, such as the Metropolis-Hastings algorithm and the Gibbs sampler, as well as a new method that involves likelihood approximation. It is found that standard algorithms perform well in some situations but can exhibit serious convergence difficulties in others. The inferences that we obtain are in broad agreement with estimates obtained by other methods where they are available. However, we can also provide inferences for parameters which have not been reported in previous analyses.

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