Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model

In this paper, we study the global dynamics of a delayed SIRS epidemic model for transmission of disease with a class of nonlinear incidence rates of the form βS(t)∫ 0 hf(τ)G(I(t-τ))dτ. Applying Lyapunov functional techniques in the recent paper [Y. Nakata, Y. Enatsu, Y. Muroya, On the global stabil...

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Detalhes bibliográficos
Autores: Enatsu, Y., Nakata, Y., Muroya, Y.
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2012
País:España
Recursos:Basque Center for Applied Mathematics (BCAM)
Repositório:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/416
Acesso em linha:http://hdl.handle.net/20.500.11824/416
Access Level:Acceso aberto
Palavra-chave:Distributed delays
Global asymptotic stability
Lyapunov functional
Nonlinear incidence rate
SIRS epidemic model
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spelling Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic modelEnatsu, Y.Nakata, Y.Muroya, Y.Distributed delaysGlobal asymptotic stabilityLyapunov functionalNonlinear incidence rateSIRS epidemic modelIn this paper, we study the global dynamics of a delayed SIRS epidemic model for transmission of disease with a class of nonlinear incidence rates of the form βS(t)∫ 0 hf(τ)G(I(t-τ))dτ. Applying Lyapunov functional techniques in the recent paper [Y. Nakata, Y. Enatsu, Y. Muroya, On the global stability of an SIRS epidemic model with distributed delays, Discrete Contin. Dyn. Syst. Supplement (2011) 11191128], we establish sufficient conditions of the rate of immunity loss for the global asymptotic stability of an endemic equilibrium for the model. In particular, we offer a unified construction of Lyapunov functionals for both cases of R 0 ≤ 1 and R 0 > 1, where R 0 is the basic reproduction number.201720172012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/416reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84859101715&doi=10.1016%2fj.nonrwa.2012.01.007&partnerID=40&md5=5dc6900e3a7ae59be6c3b17037632c36Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/4162026-06-19T12:47:47Z
dc.title.none.fl_str_mv Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model
title Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model
spellingShingle Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model
Enatsu, Y.
Distributed delays
Global asymptotic stability
Lyapunov functional
Nonlinear incidence rate
SIRS epidemic model
title_short Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model
title_full Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model
title_fullStr Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model
title_full_unstemmed Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model
title_sort Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model
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
SIRS epidemic model
topic Distributed delays
Global asymptotic stability
Lyapunov functional
Nonlinear incidence rate
SIRS epidemic model
description In this paper, we study the global dynamics of a delayed SIRS epidemic model for transmission of disease with a class of nonlinear incidence rates of the form βS(t)∫ 0 hf(τ)G(I(t-τ))dτ. Applying Lyapunov functional techniques in the recent paper [Y. Nakata, Y. Enatsu, Y. Muroya, On the global stability of an SIRS epidemic model with distributed delays, Discrete Contin. Dyn. Syst. Supplement (2011) 11191128], we establish sufficient conditions of the rate of immunity loss for the global asymptotic stability of an endemic equilibrium for the model. In particular, we offer a unified construction of Lyapunov functionals for both cases of R 0 ≤ 1 and R 0 > 1, where R 0 is the basic reproduction number.
publishDate 2012
dc.date.none.fl_str_mv 2012
2017
2017
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dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/416
url http://hdl.handle.net/20.500.11824/416
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-s2.0-84859101715&doi=10.1016%2fj.nonrwa.2012.01.007&partnerID=40&md5=5dc6900e3a7ae59be6c3b17037632c36
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/
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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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