DJIDJOU DEMASSE, Ramsès; DUCROT, Arnaud; FABRE, Frédéric

doi:10.1142/S0218202517500051

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DJIDJOU DEMASSE, Ramsès
Unité Mixte de Recherche en Santé Végétale (INRA/ENITA) [UMRSV]

DUCROT, Arnaud
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]

FABRE, Frédéric
Unité Mixte de Recherche en Santé Végétale (INRA/ENITA) [UMRSV]

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Article de revue

Ce document a été publié dans

Mathematical Models and Methods in Applied Sciences. 2017, vol. 27, n° 2, p. 385-426

World Scientific Publishing

Résumé en anglais

In this paper, we construct a model to describe the evolutionary epidemiology of spore producing asexual plant pathogens in a homogeneous host population. By considering the evolution in the space of the pathogen phenotypic values, we derive an integro-differential equation with nonlocal mutation terms. Our first main result is concerned with the existence and uniqueness of the endemic steady state of the model. Next assuming that the mutation kernel depends on a small parameter ε>0ε>0 (the variance of the dispersion into the space of the pathogen phenotypic values), we investigate the concentration properties of the endemic steady state in the space of phenotypic values. In the context of this work, several Evolutionary Attractors (EAs) (as defined in classical adaptive dynamics) may exist. However, in rather general situations, our results show that only one EA persists when the populations are at equilibrium and when εε is small enough. Our analysis strongly relies on a refined description of the spectral properties of some integral operator with a highly concentrated kernel. We conclude the paper by presenting some numerical simulations of the model to illustrate this concentration phenomenon.< Réduire

Mots clés

épidémiologie

analyse phénotypique

dynamique des populations

Mots clés en anglais

evolutionary epidemiology

spore producing pathogens

population dynamics

concentration phenomenon

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193541

DOI

http://dx.doi.org/10.1142/S0218202517500051

Projet Européen

AgreenSkills+

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251