Propagation of Epidemics Along Lines with Fast Diffusion

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 R-0 is close to 1. We also prove here further qualitative features of the final state, showing the influence of the line.

Automated summary

The article discusses the phenomenon of epidemics spreading along communication lines and proposes a new model for quantitative analysis. In the model, an additional pathway composed of infected individuals traveling is added, along with constant exchanges of populations between the line and domain. The study establishes the existence of a minimal spreading speed, which can be quite large even when the basic reproduction number is close to 1.