Modelling The Immune Response And Viral Dynamics In HBV Infection

Abstract

Hepatitis B virus (HBV) infection remains a significant global public health challenge, affecting approximately 250 million people worldwide and leading to severe liver complications including cirrhosis and hepatocellular carcinoma. This study presents a deterministic compartmental mathematical model to investigate the transmission dynamics of HBV infection and its progression to liver cirrhosis. The total population is divided into six compartments: susceptible (S), exposed (E), infected (I), hospitalized (H), cirrhotic (C), and recovered (R). The model incorporates key epidemiological parameters including recruitment rate, transmission rate, progression rates between disease stages, recovery rates, and disease-induced mortality rates. We establish the well-posedness of the model by proving the positivity and boundedness of solutions. The basic reproduction number R₀ is derived using the next-generation matrix approach, serving as a threshold parameter for disease persistence or elimination. Rigorous stability analysis demonstrates that the disease-free equilibrium is locally and globally asymptotically stable when R₀ < 1, indicating disease eradication, while the endemic equilibrium is globally asymptotically stable when R₀ > 1, signifying sustained transmission. Sensitivity analysis identifies the transmission rate β and recruitment rate Λ as the most influential parameters affecting disease dynamics. Numerical simulations using MATLAB validate the theoretical findings and illustrate the temporal evolution of all population compartments under different parameter scenarios. The results emphasize the critical importance of early diagnosis, timely medical intervention, and integrated control strategies including vaccination and antiviral therapy in reducing HBV burden. This modelling framework provides valuable insights for public health policymakers and can be extended to study other chronic infectious diseases with similar transmission patterns.