# American Institute of Mathematical Sciences

doi: 10.3934/dcds.2021064

## Asymptotic speed of spread for a nonlocal evolutionary-epidemic system

 1 Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France 2 CNRS, IMB, UMR 5251, F-33400 Talence, France 3 Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France

* Corresponding author: Jean-Baptiste Burie

Received  October 2020 Revised  February 2021 Published  March 2021

We investigate spreading properties of solutions for a spatially distributed system of equations modelling the evolutionary epidemiology of plant-pathogen interactions. In this work the mutation process is described using a non-local convolution operator in the phenotype space. Initially equipped with a localized amount of infection, we prove that spreading occurs with a definite spreading speed that coincides with the minimal speed of the travelling wave solutions discussed in [1]. Moreover, the solution of the Cauchy problem asymptotically converges to some specific function for which the moving frame variable and the phenotype one are separated.

Citation: Lara Abi Rizk, Jean-Baptiste Burie, Arnaud Ducrot. Asymptotic speed of spread for a nonlocal evolutionary-epidemic system. Discrete & Continuous Dynamical Systems, doi: 10.3934/dcds.2021064
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