Analysis of a SIRI epidemic model with distributed delay and relapse
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/26475 |
Resumo: | We investigate the global behaviour of a SIRI epidemic model with distributed delay and relapse. From the theory of functional differential equations with delay, we prove that the solution of the system is unique, bounded, and positive, for all time. The basic reproduction number R0 for the model is computed. By means of the direct Lyapunov method and LaSalle invariance principle, we prove that the disease free equilibrium is globally asymptotically stable when R0 < 1. Moreover,we show that there is a unique endemic equilibrium, which is globally asymptotically stable, when R0 > 1. |
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Analysis of a SIRI epidemic model with distributed delay and relapseGlobal stabilityNonlinear incidence functionDistributed delayLyapunov functionalsRelapseWe investigate the global behaviour of a SIRI epidemic model with distributed delay and relapse. From the theory of functional differential equations with delay, we prove that the solution of the system is unique, bounded, and positive, for all time. The basic reproduction number R0 for the model is computed. By means of the direct Lyapunov method and LaSalle invariance principle, we prove that the disease free equilibrium is globally asymptotically stable when R0 < 1. Moreover,we show that there is a unique endemic equilibrium, which is globally asymptotically stable, when R0 > 1.IAPress2019-09-03T16:17:02Z2019-09-01T00:00:00Z2019-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/26475eng2311-004X10.19139/soic-2310-5070-831Elazzouzi, AbdelhaiAlaoui, Abdesslem LamraniTilioua, MouhcineTorres, Delfim F. M.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:51:16Zoai:ria.ua.pt:10773/26475Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:59:27.463556Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Analysis of a SIRI epidemic model with distributed delay and relapse |
title |
Analysis of a SIRI epidemic model with distributed delay and relapse |
spellingShingle |
Analysis of a SIRI epidemic model with distributed delay and relapse Elazzouzi, Abdelhai Global stability Nonlinear incidence function Distributed delay Lyapunov functionals Relapse |
title_short |
Analysis of a SIRI epidemic model with distributed delay and relapse |
title_full |
Analysis of a SIRI epidemic model with distributed delay and relapse |
title_fullStr |
Analysis of a SIRI epidemic model with distributed delay and relapse |
title_full_unstemmed |
Analysis of a SIRI epidemic model with distributed delay and relapse |
title_sort |
Analysis of a SIRI epidemic model with distributed delay and relapse |
author |
Elazzouzi, Abdelhai |
author_facet |
Elazzouzi, Abdelhai Alaoui, Abdesslem Lamrani Tilioua, Mouhcine Torres, Delfim F. M. |
author_role |
author |
author2 |
Alaoui, Abdesslem Lamrani Tilioua, Mouhcine Torres, Delfim F. M. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Elazzouzi, Abdelhai Alaoui, Abdesslem Lamrani Tilioua, Mouhcine Torres, Delfim F. M. |
dc.subject.por.fl_str_mv |
Global stability Nonlinear incidence function Distributed delay Lyapunov functionals Relapse |
topic |
Global stability Nonlinear incidence function Distributed delay Lyapunov functionals Relapse |
description |
We investigate the global behaviour of a SIRI epidemic model with distributed delay and relapse. From the theory of functional differential equations with delay, we prove that the solution of the system is unique, bounded, and positive, for all time. The basic reproduction number R0 for the model is computed. By means of the direct Lyapunov method and LaSalle invariance principle, we prove that the disease free equilibrium is globally asymptotically stable when R0 < 1. Moreover,we show that there is a unique endemic equilibrium, which is globally asymptotically stable, when R0 > 1. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-09-03T16:17:02Z 2019-09-01T00:00:00Z 2019-09 |
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://hdl.handle.net/10773/26475 |
url |
http://hdl.handle.net/10773/26475 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2311-004X 10.19139/soic-2310-5070-831 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
IAPress |
publisher.none.fl_str_mv |
IAPress |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799137649277009920 |