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Complete global stability for an SIRS epidemic model with generalized non-linear incidence and vaccination. (English) Zbl 1237.92054
Summary: This paper deals with global dynamics of an SIRS epidemic model for infections with non permanent acquired immunity. The SIRS model studied here incorporates a preventive vaccination and generalized nonlinear incidence rate as well as the disease-related death. Lyapunov functions are used to show that the disease-free equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one, and that there is an endemic equilibrium state which is globally asymptotically stable when it is greater than one.

##### MSC:
 92D30 Epidemiology 34D23 Global stability of solutions to ordinary differential equations 92C60 Medical epidemiology 65C20 Probabilistic models, generic numerical methods in probability and statistics
##### Keywords:
vaccination; reproduction number; Lyapunov function
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##### References:
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