*(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.

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