Modelling Hepatitis B Virus Transmission Dynamics In The Presence of Vaccination and Treatment

Abstract

Hepatitis B is a global threat as over a billion people have been infected and about 300 million people die annually across the world. In this paper, a mathematical model for the transmission dynamics of hepatitis B virus infection considering vaccination and treatment as control parameters in the host population is presented. First, the disease-free equilibrium state of the model was determined. The next generation method was used to determine the basic reproduction number,  as a threshold parameter, in terms of the given model parameters.  was analytically evaluated for its sensitivity to vaccination and treatment parameters. It was proved that the disease-free equilibrium state is locally asymptotically stable if the  is below unity, otherwise, it is unstable. Local stability of the endemic equilibrium state was established using the centre manifold theory. The analytical results of the  show that increasing the proportion of people who receive vaccines, either at birth or later in life, reduces it below unity. Similarly, increasing the proportion of carriers who receive treatment achieves the same purpose. The result of the local stability analysis of the disease-free equilibrium state shows that the disease can be eliminated if  is below unity. The result of the centre manifold theory on the endemic equilibrium state shows that the disease can persist as the value of  increases above one. The findings of this study strongly suggest a combination of effective vaccination and treatment as a control strategy is crucial to the success of HBV disease control.