Mathematical modelling of the transmission dynamics of hepatitis B virus in the presence of imperfect vaccination

Abstract

Hepatitis B infection remains a global problem since the 1990s and the reasons for which disease is still in existence remain poorly understood. However, understanding the important role played by vaccination in the transmission dynamics of Hepatitis B virus is critical to its control and management. In this paper, an epidemiological model is proposed to model the spread of the Hepatitis B virus disease in the presence of imperfect vaccination. The basic reproduction number, R₀ and the equilibria of the model are determined and the stabilities of the equilibria determined. It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable when R₀ < 1 while the endemic equilibrium point is proved to be locally asymptotically stable when R₀ > 1. The model is also shown to exhibit a backward bifurcation phenomenon. Numerical simulations are carried out and it is observed that increasing both the vaccination and treatment rates reduces the populations of both the acutely infected and chronic carriers which eventually leads to the containment of the disease. We conclude that the combination of both vaccination and treatment with the use of a vaccine with a high efficacy is essential in the control of Hepatitis B virus disease.