Developing a Mathematical Model for Analyzing Hepatitis B Virus Transmission Dynamics and Control.
Abstract:
This study presents the development and analysis of a deterministic model for the transmission dynamics and control of hepatitis B virus (HBV) in a population with non-equal birth and death removal rates, incorporating factors such as vertical transmission, sexual maturity, condom usage, and vaccination coverage influenced by a public enlightenment campaign. The effective basic reproduction number is derived to assess disease transmission control, and conditions for local and global stability of the disease-free equilibrium are established. Bifurcation analysis using center manifold theory reveals a forward bifurcation for the model. Sensitivity analysis highlights the significant impact of birth and death removal rates, HBV sexual transmission probability per contact rate, and average total sexual contacts rate on HBV transmission dynamics in any population. Vaccination, condom usage, reduced average total sexual contacts, and birth rates emerge as effective strategies for HBV control. Numerical simulations validate the analytical results and demonstrate that HBV vaccination of new births alone, even at any coverage rate, is insufficient for disease control. However, vaccinating sexually active susceptible individuals at approximately 30% coverage rate can effectively control the disease. In conclusion, the current control strategy for HBV in Nigeria is found to be insufficient in reducing disease morbidity, and two feasible solutions to the HBV infection problem are proposed.
Developing a Mathematical Model for Analyzing Hepatitis B Virus Transmission Dynamics and Control.