We study the basic reproduction numbers for a class of reaction-diffusion epidemic models that are developed from autonomous ODE systems. We present a general numerical framework to compute such basic reproduction numbers; meanwhile, the numerical formulation provides useful insight into their characterizations. Using matrix analysis, we show that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important cases that include, among others, a single infected compartment, constant diffusion rates, uniform diffusion patterns among the infected compartments, and partial diffusion in the system.

中文翻译：

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一类反应扩散流行病模型的基本再现数

我们研究了一类由自主 ODE 系统开发的反应扩散流行模型的基本再生数。我们提出了一个通用的数值框架来计算这种基本的繁殖数；同时，数值公式提供了对其表征的有用见解。使用矩阵分析，我们表明这些 PDE 模型及其相关 ODE 模型在几个重要情况下的基本再生数是相同的，其中包括单个受感染隔室、恒定扩散速率、受感染隔室之间的均匀扩散模式、和系统中的部分扩散。