We formulate a coupled system of renewal equations for the forces of infections in interacting subgroups through a contact network. We use the theory of order-preserving and sub-homogeneous discrete dynamical systems to show the existence and uniqueness of the disease outbreak final sizes in the sub-populations. We illustrate the general theory through a simple SIR model with exponentially and non-exponentially distributed infectious period.

中文翻译：

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通过接触网络的感染力更新方程的耦合系统

我们为通过接触网络相互作用的亚组中的感染力制定了一个更新方程的耦合系统。我们使用顺序保持和亚齐次离散动力系统的理论来显示亚群中疾病暴发最终规模的存在和唯一性。我们通过具有指数和非指数分布的传染期的简单SIR模型来说明一般理论。