MODELING THE IMMUNE RESPONSE AND VIRAL DYNAMICS IN HBV INFECTION

Abstract

This study develops a deterministic mathematical model to describe the transmission dynamics of Hepatitis B Virus (HBV) infection and its progression toward liver cirrhosis. The proposed model divides the population into six compartments: susceptible, exposed, infected, hospitalized, cirrhotic, and recovered individuals. The well-posedness of the model is established by demonstrating the positivity and boundedness of its solutions. The disease-free equilibrium and the basic reproduction number, (R_0), are derived using the next-generation matrix approach. The stability analysis shows that the disease-free equilibrium is locally and globally asymptotically stable when (R_0<1), whereas the endemic equilibrium is stable when (R_0>1). Furthermore, sensitivity analysis is conducted to identify the parameters that have the greatest influence on (R_0), while numerical simulations are performed to illustrate the behavior of the model under different parameter conditions. The results indicate that reducing the transmission rate and improving prevention, hospitalization, and treatment-related interventions can contribute to controlling HBV transmission and reducing the progression of infection toward liver cirrhosis. The proposed model provides a mathematical framework for understanding HBV dynamics and evaluating potential strategies for disease control.