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Permanence of an SIR epidemic model with distributed time delays. (English) Zbl 1014.92033

Summary: We consider permanence of an SIR epidemic model with distributed time delays. Based on some known techniques on limit sets of differential dynamical systems, we show that, for any time delay, the SIR epidemic model is permanent if and only if an endemic equilibrium exits.

MSC:

92D30 Epidemiology
34K20 Stability theory of functional-differential equations
37N25 Dynamical systems in biology
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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