Reaction-Diffusion Modeling and Numerical Analysis of Hepatitis B Dynamics With Treatment and Vaccination Strategies

This study develops a novel reaction-diffusion model to analyze the spatiotemporal transmission dynamics of hepatitis B virus (HBV), explicitly incorporating treatment and vaccination strategies. The model divides the population into seven epidemiological compartments and integrates spatial diffusion to capture the effects of individual movement and regional heterogeneity. We derive the basic reproduction number 𝑅0 and analyze the stability of disease-free and endemic equilibria. Sensitivity analysis identifies critical parameters influencing disease spread, offering guidance for targeted interventions. Numerical simulations, conducted using a positivity-preserving finite difference scheme, demonstrate the impact of treatment and vaccination on disease containment. Results reveal how spatial mobility and medical interventions interact to shape HBV dynamics, emphasizing the importance of geographically informed health strategies. This framework provides new insights into controlling HBV through integrated spatial and epidemiological modeling.