A Mathematical Model of Hepatitis B Virus Transmission Dynamics considering HBV Mutants
O. Abu & E. Jalija
Department of Mathematics and Statistics
Federal Polytechnic, Idah, Nigeria
Corresponding Author: O. Abu
ABSTRACT
Hepatitis B is a global threat as approximately one third of the world’s population has serological evidence of past or present infection with hepatitis B virus (HBV) and 350–400 million people are chronic HBV surface antigen (HBs Ag) carriers In this paper, a mathematical model for the transmission dynamics of hepatitis B virus infection considering HBV mutants is presented. First, the disease-free equilibrium state of the model was determined. The next generation method was used to compute the basic reproduction number, as a threshold parameter, in terms of the given model parameters. It was proved that the disease-free equilibrium state is locally asymptotically stable if the is below unity. Local stability of the endemic equilibrium state was established using the centre manifold theory. 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 results of numerical simulations show that the impact of carriers with HBV mutants can be significant. The findings of this study strongly suggest that effective intervention should be put in place to reduce the proportion of carriers with HBV mutants to the barest minimum.
Keywords: Mathematical model, disease-free equilibrium, endemic equilibrium, centre manifold
