Mathematical Modeling for Transmission Dynamics of Hepatitis B Virus

Abstract

 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 compart mental mathematical model based on a system of linear differential equa
tion is formulated to describe the spread of HBV in a population. The basic reproduction number R0 is derived to characterized the transmis sion potential of the disease. Analytical results show that the disease-freeequilibrium (DFE) is locally asymptotically stable when R0 < 1 and become unstable when R0 > 1, while the endemic equilibrium (EE) existsand 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 SFDscheme 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.