Mathematical modeling and simulation of hepatitis B transmission dynamics with passive immunity and control strategies.

Hepatitis B Virus (HBV) is a continued threat to mankind's health killing hundreds of thousands of people every year and thus calls for control and prevention measures to be put in place. This research constructs a deterministic mathematical model to capture the transmission dynamics of HBV and embracing the control measures including universal immunization of the infants at birth, screening, as well as treatment of the both the acute and chronic cases. We employ the NGM technique to estimate the control reproduction number Rc and also study the stability of the IFE. The study findings revealed the fact that the IFE is both locally and globally asymptotic stability if c < 1. The results derived from analytical and numerical analysis revealed that having higher vaccination coverage, better screening and more efforts invested in the treatment active reduce HBV cases. Also, exposure to past immunities through passive action on the part of newborns has a significant responsibility to bear concerning the management of HBV transference. Therefore, our research findings indicate that multiple interventions can go a long way towards eliminating the ravages of HBV in the general population and consequently enhancing the general wellbeing of the population. The future work includes taking co-infections, different degrees of compliance, and age structured models into account for the elaboration of the study. Some of the limitations include: A Constant mixing volume is assumed while this may not be true throughout the entire volume Mixing parameters are also assumed to be constant while in reality they may not be so.