Pulse vaccination in the periodic infection rate sir epidemic model

Zhen Jin, Mainul Haque, Quanxing Liu

Research output: Journal PublicationArticlepeer-review

36 Citations (Scopus)


In this paper a pulse vaccination SIR model with periodic infection rate β(t) is studied. The basic reproductive number R 0 is defined. The dynamical behavior of the model is analyzed. It is proved that the infection-free periodic solution is globally stable if R 0 < 1. The infection-free periodic solution is unstable and the disease will uniform persistence when R 0 > 1. We use standard bifurcation theory to show the existence of the positive periodic solution when R 0 → 1 +. Numerical simulation can give suggestion, the system has a unique positive periodic, and it is globally stable when R 0 > 1.

Original languageEnglish
Pages (from-to)409-432
Number of pages24
JournalInternational Journal of Biomathematics
Issue number4
Publication statusPublished - Dec 2008
Externally publishedYes


  • Epidemic model
  • globally stable
  • pulse vaccination
  • the basic reproductive number
  • the infection-free periodic solution
  • the positive periodic solution
  • uniform persistence

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics


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