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 language | English |
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Pages (from-to) | e779-e788 |
Journal | Nonlinear Analysis, Theory, Methods and Applications |
Volume | 63 |
Issue number | 5-7 |
DOIs | |
Publication status | Published - Nov 30 2005 |
Keywords
- Equilibrium and Stability analysis
- Hopf bifurcation
- SIRS epidemic model
- Time delay
- Vaccination
ASJC Scopus subject areas
- Analysis
- Applied Mathematics