Global dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phase
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.3934/mbe.2020067 http://hdl.handle.net/11449/201355 |
Resumo: | In 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. |
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Global dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phaseAge-structured PDEBasic reproduction numberDelay differential-difference systemLocal and global stabilityLyapunov functionalSIR epidemic modelIn 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.Inria CNRS UMR 5208 Institut Camille Jordan, Universite Lyon 1Laboratoire d'Analyse Nonlineaire et Mathematiques Appliquees Universite de Tlemcen-TlemcenDepartment of Biostatistics São Paulo State University (UNESP)Department of Biostatistics São Paulo State University (UNESP)Institut Camille JordanUniversite de Tlemcen-TlemcenUniversidade Estadual Paulista (Unesp)Adimy, MostafaChekroun, AbdennasserFerreira, Claudia Pio [UNESP]2020-12-12T02:30:27Z2020-12-12T02:30:27Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1329-1354http://dx.doi.org/10.3934/mbe.2020067Mathematical Biosciences and Engineering, v. 17, n. 2, p. 1329-1354, 2020.1551-00181547-1063http://hdl.handle.net/11449/20135510.3934/mbe.20200672-s2.0-8507567033320527496982046170000-0002-9404-6098Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMathematical Biosciences and Engineeringinfo:eu-repo/semantics/openAccess2021-11-17T14:19:39Zoai:repositorio.unesp.br:11449/201355Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-05-23T20:47:50.930033Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Global dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phase |
title |
Global dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phase |
spellingShingle |
Global dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phase Adimy, Mostafa Age-structured PDE Basic reproduction number Delay differential-difference system Local and global stability Lyapunov functional SIR epidemic model |
title_short |
Global dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phase |
title_full |
Global dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phase |
title_fullStr |
Global dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phase |
title_full_unstemmed |
Global dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phase |
title_sort |
Global dynamics of a differential-difference system: A case of Kermack-McKendrick SIR model with age-structured protection phase |
author |
Adimy, Mostafa |
author_facet |
Adimy, Mostafa Chekroun, Abdennasser Ferreira, Claudia Pio [UNESP] |
author_role |
author |
author2 |
Chekroun, Abdennasser Ferreira, Claudia Pio [UNESP] |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Institut Camille Jordan Universite de Tlemcen-Tlemcen Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Adimy, Mostafa Chekroun, Abdennasser Ferreira, Claudia Pio [UNESP] |
dc.subject.por.fl_str_mv |
Age-structured PDE Basic reproduction number Delay differential-difference system Local and global stability Lyapunov functional SIR epidemic model |
topic |
Age-structured PDE Basic reproduction number Delay differential-difference system Local and global stability Lyapunov functional SIR epidemic model |
description |
In 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. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-12T02:30:27Z 2020-12-12T02:30:27Z 2020-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.3934/mbe.2020067 Mathematical Biosciences and Engineering, v. 17, n. 2, p. 1329-1354, 2020. 1551-0018 1547-1063 http://hdl.handle.net/11449/201355 10.3934/mbe.2020067 2-s2.0-85075670333 2052749698204617 0000-0002-9404-6098 |
url |
http://dx.doi.org/10.3934/mbe.2020067 http://hdl.handle.net/11449/201355 |
identifier_str_mv |
Mathematical Biosciences and Engineering, v. 17, n. 2, p. 1329-1354, 2020. 1551-0018 1547-1063 10.3934/mbe.2020067 2-s2.0-85075670333 2052749698204617 0000-0002-9404-6098 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Mathematical Biosciences and Engineering |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
1329-1354 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1803045695997870080 |