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

Quentin Griette (1, 2, 3) , Gaël Raoul (4)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 CEFE - Centre d’Ecologie Fonctionnelle et Evolutive
3 EEE
4 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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.

Mots clés: réaction-diffusion; épidémiologie; évolution; EDP

Domaines: Equations aux dérivées partielles [math.AP]

Quentin Griette, Gaël Raoul. Existence and qualitative properties of travelling waves for an epidemiological model with mutations. Journal of Differential Equations, 2016, 260 (10), pp.7115-7151. ⟨10.1016/j.jde.2016.01.022⟩. ⟨hal-01467351⟩