论文标题
较大子社区人口的流行病爵士
SIR epidemics in populations with large sub-communities
论文作者
论文摘要
我们调查了SIR（易感性$ \ to $感染$ \ to Recovery $ focouncted $）的最终结果特性，该模型定义在大型亚社区人群中，在社区内部，社区内部疾病传播的较强。我们的分析涉及通过在社区之间传播的一系列社区内爆发链对流行过程的近似。我们为个人数量以及受影响的社区数量和所谓的爆发严重程度提供了大量和中心极限类型的结果。这些结果是有效的，因为社区的规模倾向于无穷大，社区的数量固定或趋向于无穷大。即使在大型类型限制的定律中，社区之间的连接较弱也会导致随机性。作为证据的一部分，我们还获得了有关标准SIR流行病的预期分数收敛速率的新结果，该结果是其大人种的限制。
We investigate final outcome properties of an SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a population of large sub-communities in which there is stronger disease transmission within the communities than between them. Our analysis involves approximation of the epidemic process by a chain of within-community large outbreaks spreading between the communities. We derive law of large numbers and central limit type results for the number of individuals and the number of communities affected and the so-called severity of the outbreak. These results are valid as the size of communities tends to infinity, with the number of communities either fixed or also tending to infinity. The weaker between-community connections lead to randomness even in the law of large numbers type limit. As part of our proofs we also obtain a new result concerning the rate of convergence of the expected fraction infected in a standard SIR epidemic to its large-population limit.
