BURIE, Jean-Baptiste; DUCROT, Arnaud; GRIETTE, Quentin; RICHARD, Quentin

doi:10.1016/j.jde.2020.08.029

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BURIE, Jean-Baptiste
Institut de Mathématiques de Bordeaux [IMB]

DUCROT, Arnaud
Laboratoire de Mathématiques Appliquées du Havre [LMAH]

GRIETTE, Quentin
Institut de Mathématiques de Bordeaux [IMB]

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Document de travail - Pré-publication

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In this work we consider an epidemic system modelling the evolution of a spore-producing pathogen within a multi-host population of plants. Here we focus our analysis on the study of the stationary states. We first discuss the existence of such nontrivial states by using the theory of global attractors. Then we introduce a small parameter epsilon that characterises the width of the mutation kernel, and we describe the asymptotic shape of steady states with respect to epsilon. In particular, we show that the distribution of spores converges to the singular measure concentrated on the maxima of fitness of the pathogen in each plant population. This asymptotic description allows us to show the local stability of each of the positive steady states in the regime of narrow mutations, from which we deduce a uniqueness result for the nontrivial stationary states by means of a topological degree argument. These analyses rely on a careful investigation of the spectral properties of some non-local operators.< Réduire

Mots clés en anglais

Nonlocal equation

steady state solutions

epidemiology

degree theory

concentration phenomenon

population genetics

population genetics 2010 Mathematical Subject Classification: 35B40

35R09

47H11

92D10

92D30

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Concentration estimates in a multi-host epidemiological model structured by phenotypic traits

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