We consider a two-patch epidemiological system where individuals can move from one patch to another, and local interactions between the individuals within a patch are governed by the classical SIRS model. When the time-scale associated with migration is much smaller than the time-scale associated with infection, aggregation methods can be used to simplify the initial complete model formulated as a system of ordinary differential equations. Analysis of the aggregated model then shows that the two-patch basic reproduction rate is smaller than the 1 patch one. We extend this result to a linear chain of P patches (P > 2). These results are illustrated by some examples for which numerical integration of the system of ordinary differential equations is performed. Simulations of an individual based model implemented with a multi-agent system are also carried out.

中文翻译：

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具有快速迁移的多斑块 SIRS 模型中斑块数量对基本繁殖率的影响

我们考虑一个双补丁流行病学系统，其中个人可以从一个补丁移动到另一个补丁，并且补丁内个人之间的局部相互作用由经典的 SIRS 模型控制。当与迁移相关的时间尺度远小于与感染相关的时间尺度时，可以使用聚合方法来简化表示为常微分方程组的初始完整模型。然后对聚合模型的分析表明，两块基本繁殖率小于 1 块一。我们将此结果扩展到 P 个补丁的线性链 (P > 2)。这些结果通过对常微分方程组进行数值积分的一些例子来说明。