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

  • Authors

    • Amos Ogunsola Ladoke Akintola University of Technology, Ogbomoso, Nigeria
    • Olukayode Adebimpe Landmark University, Omuaran, Nigeria
    • Bolaji Popoola Federal College of Education, Osiele, Nigeria
  • Basic Reproduction Number, Dulac’s Criterion, Epidemic Model, Lyapunov Function, Poincare- Bendixson Theorem, Vaccination.
  • 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.

  • References

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  • How to Cite

    Ogunsola, A., Adebimpe, O., & Popoola, B. (2014). Dynamical analysis of an epidemic model with saturated incidence rate and vaccination. International Journal of Advanced Mathematical Sciences, 2(3), 137-143. https://doi.org/10.14419/ijams.v2i3.3363