Modelling Hepatitis B virus in the Presence of Regular Interventions.

Abstract

Hepatitis B infection remains a global problem since the 1990s in Asia and Africa and the reasons for which the hepatitis B virus disease is still in existence remains poorly understood. Mathematical models of HBV transmission dynamics have focused on the influence of prevention and control measures including vaccination, antiviral treatment and linkage to care in certain regions and countries. However, understanding the important role played by imperfect vaccination in describing the hepatitis B virus transmission dynamics is beneficial as a control strategy. In this study, an SV ICTR epidemiological model is proposed to model the spread of the hepatitis B virus disease. The basic reproduction number, R0 and the equilibria of the proposed model are discussed. 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. However, when R0 = 1, the model system shows a backward bifurcation phenomenon. Results of the numerical simulations reveal that increasing both the vaccination and treatment rates reduces the populations of both the acutely infected and chronic carriers which eventually fall to zero over a given period. Hence, combining both vaccination and treatment with the use of a vaccine with high vaccine efficacy are essential in controlling the hepatitis B virus disease.