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Stability of periodic solutions for an SIS model with pulse vaccination. (English) Zbl 1045.92042
Summary: Pulse vaccination is an important strategy for the elimination of infectious diseases. A mathematical SIS model with pulse vaccination is formulated in this paper. The dynamical behavior of the model is studied, and the basic reproductive number $R_0$ is defined. It is proved that the disease-free periodic solution is stable if $R_0 < 1$, and is unstable if $R_0 > 1$. The global stability of the disease-free periodic solution is studied and a sufficient condition is obtained. The existence and stability of endemic periodic solutions are investigated analytically and numerically.

##### MSC:
 92D30 Epidemiology 34C25 Periodic solutions of ODE 34D23 Global stability of ODE 34D05 Asymptotic stability of ODE
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##### References:
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