Advanced mathematical modeling of hepatitis B transmission dynamics with and without diffusion effect using real data from Thailand

This paper introduces a sophisticated reaction-diffusion mathematical model to analyze the transmission dynamics of Hepatitis B. A key aspect of this study is the computation of the basic reproduction number R_0 , derived through the next-generation matrix method, providing critical insights into the disease’s transmission potential. Parameter estimation is achieved using advanced least squares curve fitting, ensuring model accuracy and reliability. The model’s unique trait lies in its application of an operator splitting approach, combining finite difference and meshless methodologies, to simulate epidemic spread with and without spatial diffusion. We rigorously examine the stability of both disease-free and endemic equilibrium states, offering a comprehensive analysis of Hepatitis B (HBV) dynamics. Beyond the mathematical formulation, our study delves into the nature of HBV, acknowledging its potential to cause both chronic and acute liver damage. We propose a novel nonlinear reaction-diffusion SVEICHR model to dissect the intricate dynamics of Hepatitis B. Crucially, the paper explores effective strategies for HBV control, focusing on preventive measures like vaccination and hospitalization. The research culminates in a practical application, showcasing the effectiveness of these strategies through simulations implemented in MATLAB. This comprehensive approach not only enhances our understanding of HBV dynamics but also provides actionable strategies for its control.