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Dynamic analysis of an SIR epidemic model with state dependent pulse vaccination. (English) Zbl 1401.92195

Summary: An SIR epidemic model with state dependent pulse vaccination is proposed in this paper. Using the Poincaré map, the differential inequality and the method of qualitative analysis, we prove the existence and the stability of positive order-1 or order-2 periodic solution for this model. Moreover, we show that there is no periodic solution with order larger than or equal to three. Numerical simulations are carried out to illustrate the feasibility of our main results and the suitability of state dependent pulse vaccination is also discussed.

MSC:

92D30 Epidemiology
92C60 Medical epidemiology
34C25 Periodic solutions to ordinary differential equations
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