流行病曲线的近似
Approximating the epidemic curve
摘要：
许多流行病传播模型都有一个共同的定性结构。在流行病的初始阶段，受感染的个体的数量可以通过一个分支过程很好地近似，在此之后，易感个体的比例遵循一个或多或少的确定性过程。在本文中，我们表明，这两个功能的后果，假设一个局部分支结构的模型，并确定性的过程本身可以确定从分布的限制随机变量与落后，易感性分支过程。考虑的例子包括随机版本的Kermack & McKendrick模型，里德-弗罗斯特模型，和Volz配置模型。
英文摘要：
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.
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