Mathematical Modeling for Transmission Dynamics of Hepatitis B Virus

Hepatitis B virus (HBV) remains a major global public health concern, motivating the use of mathematical models to better understand its transmission dynamics and control strategies. In this study, a compartmental mathematical model based on a system of linear differential equation is formulated to describe the spread of HBV in a population. The basic reproduction number R0 is derived to characterized the transmission potential of the disease. Analytical results show that the disease-free equilibrium (DFE) is locally asymptotically stable when R0 < 1 and become unstable when R0 > 1, while the endemic equilibrium (EE) exists and is stable for R0 > 1. To investigate the dynamic behavior of the model numerically, both the standard finite difference (SFD) scheme and a non-standard finite difference (NSFD) scheme are implemented. The SFD scheme exhibits conditional convergence and may produce nonphysical results for certain step sizes, whereas the proposed NSFD scheme preserves essential qualitative properties of the continuous model, including positivity and stability of solutions. A stability analysis of the NSFD scheme is also presented. Numerical simulations and comparative analysis of both schemes validate the theoretical findings and demonstrate the superior performance of the NSFD method in accurately capturing the transmission dynamics of HBV.