Analysis and Control of Hepatitis B Virus Spread with Harmonic Mean Incidence and Vertical Transmission: A Compartmental Modeling Approach
Hepatitis B (HBV) is a potentially fatal liver infection that remains a primary widespread disease around the globe, despite the availability of vaccinations, owing to ongoing obstacles such as vertical transmission and delayed treatment. In the present study, a compartmental mathematical model that accounts for the effects of vertical transmission and harmonic mean type incidence is put forward for the analysis of the transmission dynamics of HBV. The model's threshold behavior is investigated through the basic reproduction number $R_0$, and the qualitative dynamics around the disease-free and endemic equilibria are examined to establish conditions for their asymptotic local and global stability. To identify key epidemiological drivers, the global sensitivity analysis of the system is performed through the incorporation of Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficient (PRCC) methodologies. We formulate the optimal control problem using Pontryagin's maximum principle. Effective strategies for diminishing the prevalence of HBV are emphasized through numerical simulations. Numerical simulations demonstrated that optimized control measures play a significant role in reducing the number of infected individuals and increasing the recovered population. In addition, we have characterized three distinct strategies for reducing infection and observed that each has limitations in eliminating infections. However, the simultaneous administration of treatment and vaccination is useful and effective for the reduction of HBV infection.