Recurrent epidemic cycles in an infectious disease model with a time delay in loss of vaccine immunity
✍ Scribed by D. Greenhalgh; Q.J.A. Khan; F.I. Lewis
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 148 KB
- Volume
- 63
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
✦ Synopsis
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.