Epidemics propagating along roads

I report here on joint work with Jean-Michel Roquejoffre and Luca Rossi.
Epidemics of the past have been known to follow communication lines. Some recent observations report similar patterns for the Covid-19 propagation in Italy. In this talk, I will present a reaction-diffusion model to account for such effects. It consists of the classical SIR model of epidemiology with spatial diffusion to which a new compartment of “traveling infected” on a road is added. I will first describe the classical model and then discuss the effects of roads. We analyze these in terms of the distribution of infected population and speed of propagation. The proofs rely on methods we have developed in earlier work on “road/field” models for biological invasions.