Pulse vaccination in the periodic infection rate sir epidemic model

Zhen Jin, Mainul Haque, Quanxing Liu

Research output: Contribution to journalArticlepeer-review


In this paper a pulse vaccination SIR model with periodic infection rate β(t) is studied. The basic reproductive number R0 is defined. The dynamical behavior of the model is analyzed. It is proved that the infection-free periodic solution is globally stable if R0 < 1. The infection-free periodic solution is unstable and the disease will uniform persistence when R0 > 1. We use standard bifurcation theory to show the existence of the positive periodic solution when R0 → 1+. Numerical simulation can give suggestion, the system has a unique positive periodic, and it is globally stable when R0 > 1.
Original languageEnglish
Pages (from-to)409-432
JournalInternational Journal of Biomathematics
Issue number04
Publication statusPublished - 1 Dec 2008


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