Dynamical analysis of an epidemic model with saturated incidence rate and vaccination

  • Abstract
  • Keywords
  • References
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  • 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.

  • Keywords

    Basic Reproduction Number; Dulac’s Criterion; Epidemic Model; Lyapunov Function; Poincare- Bendixson Theorem; Vaccination.

  • References

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Article ID: 3363
DOI: 10.14419/ijams.v2i3.3363

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