Recurrent epidemic cycles in an infectious disease model with a time delay in loss of vaccine immunity

D. Greenhalgh*, Q. J.A. Khan, F. I. Lewis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

In this paper we look at an SIRS epidemiological model with vaccination. Although immunity gained by experiencing the disease is permanent, vaccine-induced immunity is only temporary and a fixed time after vaccination individuals return to the susceptible class. The model is described and equilibrium and stability results are shown. There are three possible equilibria: one where the population is extinct; a disease-free equilibrium where the population is at a steady level and a unique endemic equilibrium. Simulation confirms that although Hopf bifurcation is theoretically possible for realistic parameter values the simulations approach the unique endemic equilibrium.

Original languageEnglish
Pages (from-to)e779-e788
JournalNonlinear Analysis, Theory, Methods and Applications
Volume63
Issue number5-7
DOIs
Publication statusPublished - Nov 30 2005
Externally publishedYes

Keywords

  • Equilibrium and Stability analysis
  • Hopf bifurcation
  • SIRS epidemic model
  • Time delay
  • Vaccination

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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