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Zbl 1177.37089
Yuan, Sanling; Li, Bo
Global dynamics of an epidemic model with a ratio-dependent nonlinear incidence rate. (English)
[J] Discrete Dyn. Nat. Soc. 2009, Article ID 609306, 13 p. (2009). ISSN 1026-0226; ISSN 1607-887X/e

Summary: We study an epidemic model with a nonlinear incidence rate which describes the psychological effect of certain serious diseases on the community when the ratio of the number of infectives to that of the susceptibles is getting larger. The model has set up a challenging issue regarding its dynamics near the origin since it is not well defined there. By carrying out a global analysis of the model and studying the stabilities of the disease-free equilibrium and the endemic equilibrium, it is shown that either the number of infective individuals tends to zero as time evolves or the disease persists. Computer simulations are presented to illustrate the results.

MSC 2000:: *37N25 Dynamical systems in biology
92D30 Epidemiology

Keywords: epidemic model; psychological effect; incidence rate

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Zentralblatt MATH Berlin [Germany]