BACKWARD BIFURCATION OF AN SIR-SI MODEL WITH VACCINATION AND TREATMENT

Abstract

In the presence of treatment, most epidemic models demon strate behavior of backward bifurcation. This is important in epidemiology because it provides significant information for disease control. However, kost models consider only one single population. In this paper, an extended model of two populations in the form SIR-SI involving vaccination and treatment is analyzed. The analysis of local and global stability of equilibria is discussed. By using the center manifold theorem, this model has backward bifurcation behaviour when the number infected people exceeds the treatment capacity. Vaccination decreases the basic reproduction number, but does not affect the backward bifurcation behavior. This study also showed that under vaccination and treatment, an endemic equilibrium always occurs when R0>1.