Analysis of a SIRI epidemic model with distributed delay and relapse

Detalhes bibliográficos
Autor(a) principal: Elazzouzi, Abdelhai
Data de Publicação: 2019
Outros Autores: Alaoui, Abdesslem Lamrani, Tilioua, Mouhcine, Torres, Delfim F. M.
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.
id RCAP_a61adcb61ca1fbda64eba55a1c7136d7
oai_identifier_str oai:ria.ua.pt:10773/26475
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling 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
_version_ 1799137649277009920

Registros relacionados