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
Descripción
Sumario: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.