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

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14 Citations (Scopus)


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
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number5-7
Publication statusPublished - Nov 30 2005



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

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics

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