Impact of vaccination and immune response in reducing Hepatitis B-related liver disease model

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Abstract

Hepatitis B virus (HBV) infection can progress from acute infection to chronic liver disease, posing a major public health concern. In this work, a mathematical model incorporating immune response and vaccination is developed using susceptible, infected, chronic, and recovered populations. Positivity and boundedness of solutions are established, and disease-free and endemic equilibria are analyzed. The basic reproduction numbers and stability conditions are derived using the next-generation matrix and Jacobian methods. Critical thresholds are obtained as $\Upsilon^{*}$ = 0.2237 for immune response and Γ^* = 0.7466 for vaccination. Numerical simulations using the fourth-order Runge–Kutta method demonstrate that enhanced immune response and vaccination can reduce HBV infection and chronic cases. The findings provide quantitative evidence on the role of immune response and vaccination in controlling HBV transmission and disease progression.

Keywords

vaccination / disease progression / liver disease / chronic infection

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