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Stability of a delayed SIRS epidemic model with a nonlinear incidence rate. (English) Zbl 1198.34098
Summary: An SIRS epidemic model with a nonlinear incidence rate and a time delay is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. By comparison arguments, it is proved that if the basic reproductive number \(R_{0}<1\), the disease-free equilibrium is globally asymptotically stable. If \(R_{0}>1\), by means of an iteration technique, sufficient conditions are derived for the global asymptotic stability of the endemic equilibrium.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
34D23 Global stability of solutions to ordinary differential equations
92D30 Epidemiology
34K20 Stability theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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