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

In this article, we are interested in a non-monotonic system of logistic reaction-diffusion equations. This system of equations models an epidemic 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 travelling waves with minimal speed, which are usually non-monotonic. Then we provide a description of the shape of those constructed travelling waves, and relate them to some Fisher-KPP fronts with non-minimal speed.