It has long been known that epidemics can travel along communication lines, such as roads. In the current COVID-19 epidemic, it has been observed that major roads have enhanced its propagation in Italy. We propose a new simple model of propagation of epidemics which exhibits this effect and allows for a quantitative analysis. The model consists of a classical SIR model with diffusion, to which an additional compartment is added, formed by the infected individuals travelling on a line of fast diffusion. The line and the domain interact by constant exchanges of populations. A classical transformation allows us to reduce the proposed model to a system analogous to one we had previously introduced Berestycki et al. (J Math Biol 66:743–766, 2013) to describe the enhancement of biological invasions by lines of fast diffusion. We establish the existence of a minimal spreading speed, and we show that it may be quite large, even when the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0 is close to 1. We also prove here further qualitative features of the final state, showing the influence of the line.

中文翻译：

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沿着快速扩散的路线传播流行病

人们早就知道，流行病可以沿着通信线路传播，例如道路。在当前的 COVID-19 流行病中，已观察到主要道路加强了其在意大利的传播。我们提出了一种新的流行病传播简单模型，该模型展示了这种效果并允许进行定量分析。该模型由具有扩散的经典 SIR 模型组成，其中添加了一个额外的隔间，由受感染的个体在快速扩散线上行进形成。线和域通过人口的不断交换而相互作用。经典转换使我们能够将所提出的模型简化为类似于我们之前介绍的 Berestycki 等人的系统。(J Math Biol 66:743–766, 2013) 描述通过快速扩散线增强生物入侵。