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Journal Articles Discrete & Continuous Dynamical Systems - A Year : 2021

Asymptotic speed of spread for a nonlocal evolutionary-epidemic system

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Abstract

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.

Dates and versions

hal-03943486 , version 1 (17-01-2023)

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Cite

Lara Abi Rizk, Jean-Baptiste Burie, Arnaud Ducrot. Asymptotic speed of spread for a nonlocal evolutionary-epidemic system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (10), pp.4959. ⟨10.3934/dcds.2021064⟩. ⟨hal-03943486⟩
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