%0 Journal Article
%T Dynamical analysis of an epidemic model with saturated incidence rate and vaccination
%A Amos Ogunsola
%A Bolaji Popoola
%A Olukayode Adebimpe
%J -
%D 2014
%R 10.14419/ijams.v2i3.3363
%X 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.
%U https://www.sciencepubco.com/index.php/IJAMS/article/view/3363