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Travelling waves in invasion processes with pathogens

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierTools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]
dc.contributor.authorDUCROT, Arnaud
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierTools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]
dc.contributor.authorLANGLAIS, Michel
dc.date.accessioned2024-04-04T02:54:05Z
dc.date.available2024-04-04T02:54:05Z
dc.date.issued2008
dc.identifier.issn0218-2025
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192242
dc.description.abstractEnThis work is devoted to the study of a singular reaction--diffusion system arising in modelling the introduction of a lethal pathogen within an invading host population. In the absence of the pathogen the host population exhibits a bistable dynamics (or Allee effect). Earlier numerical simulations of the singular SI model under consideration have exhibited stable travelling waves and also, under some circumstances, a reversal of the wave front speed due to the introduction of the pathogen. Here we prove the existence of such travelling wave solutions, study their linear stability and give analytical conditions yielding a reversal of the wave front speed, that is the invading host population may eventually retreat following the introduction of the lethal pathogen.
dc.language.isoen
dc.publisherWorld Scientific Publishing
dc.subject.ensingular reaction-diffusion system
dc.subject.entravelling waves
dc.subject.enlinear stability
dc.subject.enfront reversal
dc.subject.eninvasion and persistence
dc.subject.enSI epidemic model
dc.title.enTravelling waves in invasion processes with pathogens
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
bordeaux.journalMathematical Models and Methods in Applied Sciences
bordeaux.page325-349
bordeaux.volume18
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00269150
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00269150v1
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=2008&rft.volume=18&rft.spage=325-349&rft.epage=325-349&rft.eissn=0218-2025&rft.issn=0218-2025&rft.au=DUCROT,%20Arnaud&LANGLAIS,%20Michel&rft.genre=article


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