Global Stability of HBV Epidemic Model

Abstract

In this paper, we present an hepatitis B model with multiple transmission ways of the acute counsel, uncounsel and carrier infection classes and derive basic reproduction number, which indicates that hepatitis B is endemic. Existence of disease free and endemic equilibrium state are carried-out. The disease free and endemic equilibrium are shown to be globally asymptotically stable. In addition, we obtained numerical simulation to verify the model predictions. The results suggest that the endemic nature of the model was stable. However, if the control measures put in place can be maximize, then the model can be used to predict the effectiveness of the prophylactic vaccination program in sustaining the population from the spread of the disease.