Permanence and extinction for a nonautonomous SIRS epidemic model with time delay. (English) Zbl 1168.34358

Summary: A nonautonomous SIRS epidemic model with time delay is studied. We introduce some new threshold values \(R_{*}\) and \(R^{*}\) and further obtain the disease will be permanent when \(R_{*}>1\) and the disease extinct when \(R^{*}<1\). Using the method of Liapunov functional, some sufficient conditions are derived for the global attractivity of the system. The known results are extended.


34K20 Stability theory of functional-differential equations
92D30 Epidemiology
Full Text: DOI


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