Two types of condition for the global stability of delayed sis epidemic models with nonlinear birth rate and disease induced death rate

We study global asymptotic stability for an SIS epidemic model with maturation delay proposed by K. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39(4) (1999) 332352. It is assumed that the population has...

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Detalles Bibliográficos
Autores: Nakata, Y., Enatsu, Y., Muroya, Y.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/422
Acceso en línea:http://hdl.handle.net/20.500.11824/422
Access Level:acceso abierto
Palabra clave:disease induced death rate
global asymptotic stability
nonlinear birth rate function
permanence
SIS epidemic models
the basic reproduction number
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spelling Two types of condition for the global stability of delayed sis epidemic models with nonlinear birth rate and disease induced death rateNakata, Y.Enatsu, Y.Muroya, Y.disease induced death rateglobal asymptotic stabilitynonlinear birth rate functionpermanenceSIS epidemic modelsthe basic reproduction numberWe study global asymptotic stability for an SIS epidemic model with maturation delay proposed by K. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39(4) (1999) 332352. It is assumed that the population has a nonlinear birth term and disease causes death of infective individuals. By using a monotone iterative method, we establish sufficient conditions for the global stability of an endemic equilibrium when it exists dependently on the monotone property of the birth rate function. Based on the analysis, we further study the model with two specific birth rate functions B 1(N) = be -aN and B 3(N) = A/N + c, where N denotes the total population. For each model, we obtain the disease induced death rate which guarantees the global stability of the endemic equilibrium and this gives a positive answer for an open problem by X. Q. Zhao and X. Zou, Threshold dynamics in a delayed SIS epidemic model, J. Math. Anal. Appl. 257(2) (2001) 282291.201720172012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/422reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84857579391&doi=10.1142%2fS1793524511001507&partnerID=40&md5=db692ce073476d756ea5cfe9e10b7730Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/4222026-06-19T12:47:47Z
dc.title.none.fl_str_mv Two types of condition for the global stability of delayed sis epidemic models with nonlinear birth rate and disease induced death rate
title Two types of condition for the global stability of delayed sis epidemic models with nonlinear birth rate and disease induced death rate
spellingShingle Two types of condition for the global stability of delayed sis epidemic models with nonlinear birth rate and disease induced death rate
Nakata, Y.
disease induced death rate
global asymptotic stability
nonlinear birth rate function
permanence
SIS epidemic models
the basic reproduction number
title_short Two types of condition for the global stability of delayed sis epidemic models with nonlinear birth rate and disease induced death rate
title_full Two types of condition for the global stability of delayed sis epidemic models with nonlinear birth rate and disease induced death rate
title_fullStr Two types of condition for the global stability of delayed sis epidemic models with nonlinear birth rate and disease induced death rate
title_full_unstemmed Two types of condition for the global stability of delayed sis epidemic models with nonlinear birth rate and disease induced death rate
title_sort Two types of condition for the global stability of delayed sis epidemic models with nonlinear birth rate and disease induced death rate
dc.creator.none.fl_str_mv Nakata, Y.
Enatsu, Y.
Muroya, Y.
author Nakata, Y.
author_facet Nakata, Y.
Enatsu, Y.
Muroya, Y.
author_role author
author2 Enatsu, Y.
Muroya, Y.
author2_role author
author
dc.subject.none.fl_str_mv disease induced death rate
global asymptotic stability
nonlinear birth rate function
permanence
SIS epidemic models
the basic reproduction number
topic disease induced death rate
global asymptotic stability
nonlinear birth rate function
permanence
SIS epidemic models
the basic reproduction number
description We study global asymptotic stability for an SIS epidemic model with maturation delay proposed by K. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39(4) (1999) 332352. It is assumed that the population has a nonlinear birth term and disease causes death of infective individuals. By using a monotone iterative method, we establish sufficient conditions for the global stability of an endemic equilibrium when it exists dependently on the monotone property of the birth rate function. Based on the analysis, we further study the model with two specific birth rate functions B 1(N) = be -aN and B 3(N) = A/N + c, where N denotes the total population. For each model, we obtain the disease induced death rate which guarantees the global stability of the endemic equilibrium and this gives a positive answer for an open problem by X. Q. Zhao and X. Zou, Threshold dynamics in a delayed SIS epidemic model, J. Math. Anal. Appl. 257(2) (2001) 282291.
publishDate 2012
dc.date.none.fl_str_mv 2012
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/20.500.11824/422
url http://hdl.handle.net/20.500.11824/422
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
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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
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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)
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