Abstract
In this paper, we extend the model of Blower et al. [1] by incorporating certain infection terms such as vaccinated individuals, treatment rate, waning rate and efficacy rate.A bifurcation analysis is performed on the vaccination model by applying a bifurcation method based on the use of center manifold theory.We determine threshold values and derive sufficient conditions for both forward and backward bifurcations.Numerical simulations were carried out and bifurcation diagrams are presented as supporting evidences of our analytical results. The obtained results show the possibility of occurrence of forward and backward bifurcations even when the basic reproduction number is less than one so that it is now possible for the disease to exist. These results suggest the need for more study on the qualitative biological mechanisms responsible for backward bifurcation.
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