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A delayed SIRS epidemic model with pulse vaccination. (English) Zbl 1152.34379

Summary: A delayed SIRS epidemic model with pulse vaccination and saturated contact rate is investigated. By using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the system. Further, by using the comparison theorem, we prove that under the condition that \(R_{0} < 1\) the infection-free periodic solution is globally attractive, and that under the condition that \(R^{\prime} > 1\) the disease is uniformly persistent, which means that after some period of time the disease will become endemic.

MSC:

34K20 Stability theory of functional-differential equations
92D30 Epidemiology
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