Hepatitis B remains a major public health challenge, especially due to its potential to progress into chronic infection and severe liver disease. This study develops a mathematical model to understand the role of Interferon therapy, particularly comparing Standard IFN-α and Pegylated IFN-α (Peg-IFN) in controlling HBV infection. The model tracks four key groups: susceptible individuals, those with acute infection, chronic cases, and recovered individuals.

We determine the basic reproduction number ( R0R_0R0​ ) and analyze the conditions under which the disease can be eradicated or persist. Our results show that when R0<1R_0 < 1R0​<1, the infection dies out, leading to a stable disease-free equilibrium (DFE). However, when R0>1R_0 > 1R0​>1, the disease persists at an endemic equilibrium (EE). Through numerical simulations, we explore how Interferon therapy influences HBV progression. The findings suggest that Peg-IFN is more effective than standard interferon due to its longer-lasting effects and stronger suppression of the virus, reducing the number of infected individuals and increasing recovery rates.

Additionally, sensitivity analysis highlights key factors—such as treatment rates, immune response, and disease progression—that influence infection dynamics. Our results reinforce the importance of early intervention and suggest that combining pegylated interferon with antiviral therapies may be the best approach for HBV control.