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Zbl 1221.34197
Huo, Hai-Feng; Ma, Zhan-Ping
Dynamics of a delayed epidemic model with non-monotonic incidence rate. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 15, No. 2, 459-468 (2010). ISSN 1007-5704

Summary: A delayed epidemic model with non-monotonic incidence rate which describes the psychological effect of certain serious on the community when the number of infectives is getting larger is studied. The disease-free equilibrium is globally asymptotically stable when $R_{0}<1$ and is globally attractive when $R_{0}=1$ are derived. On the other hand, The disease is permanent when $R_{0}>1$ is also obtained. Numerical simulation results are given to support the theoretical predictions.

MSC 2000:: *34K20 Stability theory of functional-differential equations
92D30 Epidemiology

Keywords: epidemic model; time delay; nonlinear incidence; global stability; Lyapunov functional; permanence

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Zentralblatt MATH Berlin [Germany]