Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays

In this paper, we establish the global asymptotic stability of equi-libria for an SIR model of infectious diseases with distributed time delays gov-erned by a wide class of nonlinear incidence rates. We obtain the global prop-erties of the model by proving the permanence and constructing a suitable...

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Detalles Bibliográficos
Autores: Enatsu, Y., Nakata, Y., Muroya, Y.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2011
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/440
Acceso en línea:http://hdl.handle.net/20.500.11824/440
Access Level:acceso abierto
Palabra clave:Distributed delays
Global asymptotic stability
Lyapunov functional
Nonlinear incidence rate
Permanence
SIR epidemic models
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spelling Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delaysEnatsu, Y.Nakata, Y.Muroya, Y.Distributed delaysGlobal asymptotic stabilityLyapunov functionalNonlinear incidence ratePermanenceSIR epidemic modelsIn this paper, we establish the global asymptotic stability of equi-libria for an SIR model of infectious diseases with distributed time delays gov-erned by a wide class of nonlinear incidence rates. We obtain the global prop-erties of the model by proving the permanence and constructing a suitable Lyapunov functional. Under some suitable assumptions on the nonlinear term in the incidence rate, the global dynamics of the model is completely deter-mined by the basic reproduction number R0 and the distributed delays do not influence the global dynamics of the model.201720172011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/440reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.scopus.com/inward/record.uri?eid=2-s2.0-78651244615&doi=10.3934%2fdcdsb.2011.15.61&partnerID=40&md5=06148e7435be3444ddf6f86b489b4a19Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/4402026-06-19T12:47:47Z
dc.title.none.fl_str_mv Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays
title Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays
spellingShingle Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays
Enatsu, Y.
Distributed delays
Global asymptotic stability
Lyapunov functional
Nonlinear incidence rate
Permanence
SIR epidemic models
title_short Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays
title_full Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays
title_fullStr Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays
title_full_unstemmed Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays
title_sort Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays
dc.creator.none.fl_str_mv Enatsu, Y.
Nakata, Y.
Muroya, Y.
author Enatsu, Y.
author_facet Enatsu, Y.
Nakata, Y.
Muroya, Y.
author_role author
author2 Nakata, Y.
Muroya, Y.
author2_role author
author
dc.subject.none.fl_str_mv Distributed delays
Global asymptotic stability
Lyapunov functional
Nonlinear incidence rate
Permanence
SIR epidemic models
topic Distributed delays
Global asymptotic stability
Lyapunov functional
Nonlinear incidence rate
Permanence
SIR epidemic models
description In this paper, we establish the global asymptotic stability of equi-libria for an SIR model of infectious diseases with distributed time delays gov-erned by a wide class of nonlinear incidence rates. We obtain the global prop-erties of the model by proving the permanence and constructing a suitable Lyapunov functional. Under some suitable assumptions on the nonlinear term in the incidence rate, the global dynamics of the model is completely deter-mined by the basic reproduction number R0 and the distributed delays do not influence the global dynamics of the model.
publishDate 2011
dc.date.none.fl_str_mv 2011
2017
2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/440
url http://hdl.handle.net/20.500.11824/440
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.scopus.com/inward/record.uri?eid=2-s2.0-78651244615&doi=10.3934%2fdcdsb.2011.15.61&partnerID=40&md5=06148e7435be3444ddf6f86b489b4a19
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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