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...
| Autores: | , , |
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| 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 |
| 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. |
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