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Dynamic behavior for a nonautonomous SIRS epidemic model with distributed delays. (English) Zbl 1168.92327
Summary: A nonautonomous SIRS epidemic model with distributed delays is investigated. Two new threshold values, \(R_{*}\) and \(R^{*}\) are derived. The model is permanent as \(R_{*}>1\), and \(R^{*}<1\) implies the extinction of the disease. Using the Lyapunov functional method, the global behavior of the model is studied.

MSC:
92D30 Epidemiology
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
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