A MATHEMATICAL MODEL FOR THE TRANSMISSION DYNAMICS AND CONTROL OF HEPATITIS B VIRUS

Abstract

In the work, we developed and analyzed a deterministic model for the transmission dynamics and control of hepatitis B virus (HBV) in a population with vital dynamics (birth and death removal rates are not equal), incorporating vertical transmission, sexual maturity and the effects of condom usage and vaccination coverage which are influenced by public enlightenment campaign. We obtained the effective basic reproduction number which can be used to control the transmission of the disease and hence, established the conditions for local and global stability of the disease-free equilibrium. Bifurcation analysis was carried out using centre manifold theory which revealed a forward bifurcation for the model. Furthermore, sensitivity analysis carried out shows that birth and death removal rates, HBV sexual transmission probability per contact rate and average total sexual contacts rate are highly sensitive parameters that affect the transmission dynamics of HBV in any population. This means that vaccination, condom usage, reduced-average total sexual contacts and birth rates are good strategies that can lead to controlling HBV. Numerical simulations validated the analytical results and further revealed that HBV vaccination of new births only at any coverage rate cannot bring about disease control. But vaccination of sexually active susceptible individuals at about 30% coverage rate can put the disease under control. Two feasible solutions to HBV infection problem in Nigeria were obtained as the present control strategy is not effective enough to even reduce the disease morbidity.