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

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.

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• Adaptation and migration of a population between patches

Cited by in corpus (8)

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• Travelling waves for a non-monotone bistable equation with delay: existence and oscillations
• Macroscopic limit from a structured population model to the Kirkpatrick-Barton model
• Pulsating fronts for Fisher-KPP systems with mutations as models in evolutionary epidemiology
• Two components is too simple: an example of oscillatory Fisher--KPP system with three components
• Propagation dynamics of solutions to spatially periodic reaction-diffusion systems with hybrid nonlinearity
• Generalized principal eigenvalues of space-time periodic, weakly coupled, cooperative, parabolic systems
• A note on "Existence and uniqueness of coexistence states for an elliptic system coupled in the linear part", by Hei Li-Jun, Nonlinear Anal. Real World Appl. 5, 2004