Global dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phase

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Autor(es): dc.contributorInstitut Camille Jordan-
Autor(es): dc.contributorUniversite de Tlemcen-Tlemcen-
Autor(es): dc.contributorUniversidade Estadual Paulista (Unesp)-
Autor(es): dc.creatorAdimy, Mostafa-
Autor(es): dc.creatorChekroun, Abdennasser-
Autor(es): dc.creatorFerreira, Claudia Pio [UNESP]-
Data de aceite: dc.date.accessioned2022-02-22T00:33:20Z-
Data de disponibilização: dc.date.available2022-02-22T00:33:20Z-
Data de envio: dc.date.issued2020-12-11-
Data de envio: dc.date.issued2020-12-11-
Data de envio: dc.date.issued2019-12-31-
Fonte completa do material: dc.identifierhttp://dx.doi.org/10.3934/mbe.2020067-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/11449/201355-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/11449/201355-
Descrição: dc.descriptionIn this paper, we are concerned with an epidemic model of susceptible, infected and recovered (SIR) population dynamic by considering an age-structured phase of protection with limited duration, for instance due to vaccination or drugs with temporary immunity. The model is reduced to a delay differential-difference system, where the delay is the duration of the protection phase. We investigate the local asymptotic stability of the two steady states: disease-free and endemic. We also establish when the endemic steady state exists, the uniform persistence of the disease. We construct quadratic and logarithmic Lyapunov functions to establish the global asymptotic stability of the two steady states. We prove that the global stability is completely determined by the basic reproduction number.-
Descrição: dc.descriptionInria CNRS UMR 5208 Institut Camille Jordan, Universite Lyon 1-
Descrição: dc.descriptionLaboratoire d'Analyse Nonlineaire et Mathematiques Appliquees Universite de Tlemcen-Tlemcen-
Descrição: dc.descriptionDepartment of Biostatistics São Paulo State University (UNESP)-
Descrição: dc.descriptionDepartment of Biostatistics São Paulo State University (UNESP)-
Formato: dc.format1329-1354-
Idioma: dc.languageen-
Relação: dc.relationMathematical Biosciences and Engineering-
???dc.source???: dc.sourceScopus-
Palavras-chave: dc.subjectAge-structured PDE-
Palavras-chave: dc.subjectBasic reproduction number-
Palavras-chave: dc.subjectDelay differential-difference system-
Palavras-chave: dc.subjectLocal and global stability-
Palavras-chave: dc.subjectLyapunov functional-
Palavras-chave: dc.subjectSIR epidemic model-
Título: dc.titleGlobal dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phase-
Tipo de arquivo: dc.typelivro digital-
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