Existence and qualitative properties of travelling waves for an epidemiological model with mutations

TL;DR

This paper investigates the existence and shape of non-monotonic travelling wave solutions in a reaction-diffusion epidemic model with competing pathogens and mutation, revealing their relation to Fisher-KPP fronts.

Contribution

It establishes the existence of minimal speed travelling waves in a non-monotone epidemic model with mutations and describes their qualitative properties.

Findings

Existence of minimal speed travelling waves in the model.

Travelling waves are generally non-monotonic.

Connection between these waves and Fisher-KPP fronts.

Abstract

In this article, we are interested in a non-monotone system of logistic reaction-diffusion equations. This system of equations models an epidemics where two types of pathogens are competing, and a mutation can change one type into the other with a certain rate. We show the existence of minimal speed travelling waves, that are usually non monotonic. We then provide a description of the shape of those constructed travelling waves, and relate them to some Fisher-KPP fronts with non-minimal speed.