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

Research output: Contribution to journalArticle

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
JournalNonlinear Analysis, Theory, Methods and Applications
Volume63
Issue number5-7
DOIs
Publication statusPublished - Nov 30 2005

Fingerprint

Vaccines
Vaccine
Infectious Diseases
Immunity
Time Delay
Time delay
Endemic Equilibrium
Vaccination
Cycle
Hopf bifurcation
Epidemiological Model
Hopf Bifurcation
Simulation
Model

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics

Cite this

Recurrent epidemic cycles in an infectious disease model with a time delay in loss of vaccine immunity. / Greenhalgh, D.; Khan, Q. J A; Lewis, F. I.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 63, No. 5-7, 30.11.2005.

Research output: Contribution to journalArticle

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