Factors such as seasonality and spatial connectivity affect the spread of an infectious disease. Accounting for these factors in infectious disease models provides useful information on the times and locations of greatest risk for disease outbreaks. In this investigation, stochastic multi-patch epidemic models are formulated with seasonal and demographic variability. The stochastic models are used to investigate the probability of a disease outbreak when infected individuals are introduced into one or more of the patches. Seasonal variation is included through periodic transmission and dispersal rates. Multi-type branching process approximation and application of the backward Kolmogorov differential equation lead to an estimate for the probability of a disease outbreak. This estimate is also periodic and depends on the time, the location, and the number of initial infected individuals introduced into the patch system as well as the magnitude of the transmission and dispersal rates and the connectivity between patches. Examples are given for seasonal transmission and dispersal in two and three patches.

中文翻译：

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具有人口统计学和季节性变化的多补丁随机流行病模型中的疾病出现

季节性和空间连通性等因素会影响传染病的传播。在传染病模型中考虑这些因素可以提供有关疾病爆发风险最大的时间和地点的有用信息。在这项调查中，随机多斑块流行病模型是根据季节和人口统计变化制定的。当受感染的个体被引入一个或多个补丁时，随机模型用于研究疾病爆发的可能性。季节性变化包括在周期性传播和传播率中。多类型分支过程近似和向后 Kolmogorov 微分方程的应用导致对疾病爆发概率的估计。这个估计也是周期性的，取决于时间、地点、以及引入补丁系统的初始感染个体的数量，以及传播和扩散率的大小以及补丁之间的连通性。给出了两个和三个斑块中季节性传播和散布的示例。