Propagation of epidemics along lines with fast diusion

Henri Berestycki (1) , Jean-Michel Roquejoffre (2) , Luca Rossi (1, 3)

1 CAMS - Centre d'Analyse et de Mathématique sociales
2 MIP - Mathématiques pour l'Industrie et la Physique
3 CNRS - Centre National de la Recherche Scientifique

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 eect 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 diusion. Exchanges between individuals on the line and in the rest of the domain are taken into account. A classical transformation allows us to reduce the proposed model to a system analogous to one we had previously introduced [5] to describe the enhancement of biological invasions by lines of fast diusion. We establish the existence of an asymptotic speed of spreading and we show that it may be quite large, even when the basic reproduction number R 0 is close to 1. More subtle qualitative features of the nal state, showing the important inuence of the line, are also proved here.

Mots clés: COVID-19; epidemics; SIR model; reaction-diusion system; line of fast diusion; spreading speed; nonlinear PDEs

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Henri Berestycki, Jean-Michel Roquejoffre, Luca Rossi. Propagation of epidemics along lines with fast diusion. 2020. ⟨hal-02566035⟩