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Steady state concentration for a phenotypic structured problem modeling the evolutionary epidemiology of spore producing pathogens

hal.structure.identifierUnité Mixte de Recherche en Santé Végétale (INRA/ENITA) [UMRSV]
dc.contributor.authorDJIDJOU DEMASSE, Ramsès
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierCentre National de la Recherche Scientifique [CNRS]
dc.contributor.authorDUCROT, Arnaud
hal.structure.identifierUnité Mixte de Recherche en Santé Végétale (INRA/ENITA) [UMRSV]
dc.contributor.authorFABRE, Frédéric
dc.date.accessioned2024-04-04T03:08:36Z
dc.date.available2024-04-04T03:08:36Z
dc.date.issued2017
dc.identifier.issn0218-2025
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193541
dc.description.abstractEnIn 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.
dc.language.isoen
dc.publisherWorld Scientific Publishing
dc.subjectépidémiologie
dc.subjectanalyse phénotypique
dc.subjectdynamique des populations
dc.subject.enevolutionary epidemiology
dc.subject.enspore producing pathogens
dc.subject.enpopulation dynamics
dc.subject.enconcentration phenomenon
dc.title.enSteady state concentration for a phenotypic structured problem modeling the evolutionary epidemiology of spore producing pathogens
dc.typeArticle de revue
dc.identifier.doi10.1142/S0218202517500051
dc.subject.halSciences de l'environnement/Biodiversité et Ecologie
dc.subject.halSciences de l'environnement/Environnement et Société
dc.description.sponsorshipEuropeAgreenSkills+
bordeaux.journalMathematical Models and Methods in Applied Sciences
bordeaux.page385-426
bordeaux.volume27
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01604796
hal.version1
hal.popularnon
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01604796v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Models%20and%20Methods%20in%20Applied%20Sciences&rft.date=2017&rft.volume=27&rft.issue=2&rft.spage=385-426&rft.epage=385-426&rft.eissn=0218-2025&rft.issn=0218-2025&rft.au=DJIDJOU%20DEMASSE,%20Rams%C3%A8s&DUCROT,%20Arnaud&FABRE,%20Fr%C3%A9d%C3%A9ric&rft.genre=article


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