Approximating the epidemic curve
Approximating the epidemic curve
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DOI：
10.1214/ejp.v18-2557
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发表时间：
2013-05-16
影响因子：
1.4
通讯作者：
Reinert, G.
中科院分区：
文献类型：
--
作者：
Barbour, A. D.;Reinert, G.
许多流行病传播模型都有一个共同的定性结构。流行病初期的感染人数可以通过一个分支过程很好地近似，在分支过程之后，易感个体的比例或多或少遵循一个确定性的过程。在本文中，我们证明了这两个特征都是假设模型中的局部分支结构的结果，并且确定性过程本身可以由与向后的磁化率分支过程相关的极限随机变量的分布来确定。所考虑的例子包括随机版本的Kermack&McKendrick模型、Reed-Frost模型和Volz配置模型。
Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process, after which the proportion of individuals that are susceptible follows a more or less deterministic course. In this paper, we show that both of these features are consequences of assuming a locally branching structure in the models, and that the deterministic course can itself be determined from the distribution of the limiting random variable associated with the backward, susceptibility branching process. Examples considered include a stochastic version of the Kermack & McKendrick model, the Reed-Frost model, and the Volz configuration model.