Dynamical analysis of an epidemic model with saturated incidence rate and vaccination
Abstract
An epidemic model with saturated incidence rate and vaccination is investigated. The model exhibits two equilibria namely disease-free and endemic equilibria. It is shown that if the basic reproduction number (R0) is less than unity, the disease-free equilibrium is locally asymptotically stable and in such case, the endemic equilibrium does not exist. Also, it is shown that if R0 > 1, the disease is persistent and the unique endemic equilibrium of the system with saturation incidence is locally asymptotically stable. Lyapunov function and Dulac’s criterion plus Poincare-Bendixson theorem are applied to prove the global stability of the disease-free and endemic equilibria respectively. The effect of vaccine in the model is critically looked into.
About this article
Keywords
- Basic Reproduction Number
- Dulac’s Criterion
- Epidemic Model
- Lyapunov Function
- Poincare- Bendixson Theorem
- Vaccination.
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