3rd TAGRA

Chronic Hepatitis B Virus (HBV) infection remains a major global health challenge due to its persistence and progression to severe liver diseases. This study develops and analyzes a mathematical model to investigate the long-term dynamics of chronic HBV transmission. The disease-free and endemic equilibrium points, together with the basic reproduction number $\mathfrak{R}_0$, are derived and analyzed. Stability analysis establishes that the disease-free equilibrium is locally asymptotically stable when $\mathfrak{R}_0<1$, whereas the endemic equilibrium exists and remains stable for $\mathfrak{R}_0>1$, indicating a transcritical bifurcation at $\mathfrak{R}_0=1$. Sensitivity analysis identifies the key parameters influencing disease transmission and persistence. Furthermore, an optimal control framework incorporating vaccination, treatment, and immune enhancement is formulated to determine cost-effective intervention strategies. Numerical simulations validate the theoretical results and demonstrate that the proposed control measures significantly reduce chronic HBV prevalence, providing useful insights for effective disease management and public health policy.