A compartmental model for Hepatitis B virus incorporating vaccination, medication, liver transplantation and environmental persistence

Hepatitis B virus (HBV) remains a major public health concern because of its chronic progression and severe liver complications. We propose a compartmental model describing HBV transmission that incorporates vaccination, antiviral treatment, liver transplantation and environmental contamination, accounting for both direct and indirect transmission pathways. The disease-free and endemic equilibria are derived and their local and global stability properties are analyzed. A sensitivity analysis is conducted to assess the impact of key parameters, including the infection rate, vaccination coverage and environmental persistence, on the basic reproduction number [Formula: see text] and system dynamics. Numerical simulations using the fourth-order Runge–Kutta method and a nonstandard finite difference scheme validate the theoretical results and illustrate the effectiveness of combined control strategies. These findings provide useful insights for improving HBV prevention and control policies.