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

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlinear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functi...

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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:20.500.11824/410
Acesso em linha:http://hdl.handle.net/20.500.11824/410
Access Level:Acceso aberto
Palavra-chave:Distributed delays
Global asymptotic stability
Lyapunov functional
Nonlinear incidence rate
SIRS epidemic model
Descrição
Resumo:In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlinear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear incidence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.