An introduction to stochastic epidemic models
An introduction to stochastic epidemic models
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DOI：
10.1007/978-3-540-78911-6_3
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发表时间：
2008-01-01
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影响因子：
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通讯作者：
Allen, Linda J. S.
中科院分区：
文献类型：
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作者：
Allen, Linda J. S.
基于著名的确定性SIS和SIR流行病模型，简要介绍了各种类型的随机流行病模型的建立。三种不同类型的随机模型公式进行了讨论：离散时间马尔可夫链，连续时间马尔可夫链和随机微分方程。独特的随机模型的属性：疾病灭绝的概率，疾病爆发的概率，准平稳概率分布，最终的大小分布，和预期的持续时间的流行病。本章最后讨论了两个随机配方，不能直接相关的SIS和SIR流行病模型。它们是离散时间马尔可夫链公式，应用于家庭内流行病的研究（链二项式模型）和流行病最初传播的预测（分支过程）。
A brief introduction to the formulation of various types of stochastic epidemic models is presented based on the well-known deterministic SIS and SIR epidemic models. Three different types of stochastic model formulations are discussed: discrete time Markov chain, continuous time Markov chain and stochastic differential equations. Properties unique to the stochastic models are presented: probability of disease extinction, probability of disease outbreak, quasistationary probability distribution, final size distribution, and expected duration of an epidemic. The chapter ends with a discussion of two stochastic formulations that cannot be directly related to the SIS and SIR epidemic models. They are discrete time Markov chain formulations applied in the study of epidemics within households (chain binomial models) and in the prediction of the initial spread of an epidemic (branching processes).