Modeling hepatitis B transmission dynamics with spatial diffusion and disability potential in the chronic stage

In this study, we introduce a novel reaction-diffusion epidemic model to analyze the transmission dynamics of the hepatitis B virus (HBV). The model captured the interactions between five population groups: Susceptible individuals, those in the latent stage, acutely infected individuals, chronically infected individuals, and those who have recovered, while considering the spatial movement of these groups. Chronic HBV infection contributes to severe liver diseases such as cirrhosis and hepatocellular carcinoma. It is also a major cause of long-term disability due to complications that impair daily functioning. The stability conditions for the model were derived, and the basic reproductive number, $R_0$, was calculated using the next-generation matrix approach. Numerical simulations were performed using the Crank-Nicolson operator splitting method and the Unconditionally Positivity Preserving technique to solve the model under scenarios with and without diffusion. The stability of the endemic equilibrium point was analyzed comprehensively. Detailed simulation results are presented, highlighting a comparative analysis of the numerical findings in cases where exact solutions were unavailable. The reliability of the numerical results was validated by their alignment with theoretical expectations.