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.


92D30 Epidemiology
34C25 Periodic solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
Full Text: DOI


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