Stability and Bifurcation Analysis of Endemic Equilibrium of a Mathematical Modeling of Yellow Fever Incorporating Secondary Host

Abstract

In this paper we used the Centre Manifold theorem to analyzed the local stability of Endemic Equilibrium (EE). We obtained the endemic equilibrium point in terms of forces of infection and use it to analyze for the bifurcation of the model. We carried out the bifurcation analysis of the model with four forces of infection which resulted into bifurcation diagram. The forces of infection of vector-primary host and vector-secondary host transmissions were plotted against basic reproduction number. The bifurcation diagram revealed that the model exhibit forward bifurcation.