Stochastic epidemics in dynamic populations: quasi-stationarity and extinction
Stochastic epidemics in dynamic populations: quasi-stationarity and extinction
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DOI：
10.1007/s002850000060
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发表时间：
2000-12-01
影响因子：
1.9
通讯作者：
Britton, T
中科院分区：
文献类型：
--
作者：
Andersson, H;Britton, T
经验证据表明，儿童疾病在大型社区中持续存在，而在较小的社区中，这种流行病消失了，后来又被移民重新引入)。本文讨论了一个描述传染病传播的随机模型，在一个个体死亡而新个体出生的社区中，传染病的传播给予终身免疫。疾病从准平稳状态(以非灭绝为条件)开始消亡的时间呈指数分布。随着人口规模的增长，流行病过程收敛到扩散过程。利用极限扩散的性质得到有限种群灭绝时间指数分布中的均值参数tau的近似表达式。该表达式用于研究tau如何依赖于群落的大小以及疾病/群落的某些性质：基本繁殖数以及潜伏期、感染期和寿命的均值和方差。还讨论了引入疫苗接种计划的影响，以及临界社区规模的概念，临界社区规模的定义是区分两种性质不同的行为的规模。
Empirical evidence shows chat childhood diseases persist in large communities whereas in smaller communities the epidemic goes extinct land is later reintroduced by immigration). The present paper treats a stochastic model describing the spread of an infectious disease giving life-long immunity, in a community where individuals die and new individuals an born. The time to extinction of the disease starting in quasi-stationarity (conditional on non-extinction) is exponentially distributed. As the population size grows the epidemic process converges to a diffusion process. Properties of the limiting diffusion are used to obtain an approximate expression for tau, the mean-parameter in the exponential distribution of the time to extinction for the finite population The expression is used to study how tau depends on the community size but also on certain properties of the disease/community: the basic reproduction number and the means and Variances of the latency period, infectious period and life-length. Effects of introducing a vaccination program are also discussed as is the notion of the critical community size, defined as the size which distinguishes between the two qualitatively different behaviours.