Mathematical approach to understanding HBV infection control and antiviral treatment efficacy in mice

Hepatitis B Virus (HBV) remains a global health challenge affecting millions of people worldwide. This study aimed to develop an advanced pharmacokinetic/pharmacodynamic (PK/PD) mathematical model to analyze HBV infection dynamics in mice and to evaluate antiviral treatment efficacy. Initially, we formulate a simplified HBV model incorporating two control variables, $u_{1} (t)$ and $u_{2} (t)$ to represent the drug treatment process. The control parameter $u_{1} (t)$ captures the dual role of the antiviral treatment in inhibiting viral replication and enhancing the immune response through Antibody-Dependent Cellular Cytotoxicity (ADCC), and $u_{2} (t)$ represents the drug-mediated clearance of infected cells. We then discuss the key properties, including the basic reproduction number, local and global stability of equilibria, and existence of the Hopf bifurcation. Numerical simulations were conducted to illustrate the impact of the two control parameters on the disease dynamics. Furthermore, by integrating real-world data, the model simulates the progression of infection and the effect of treatment by incorporating immune enhancement through mechanisms such as ADCC. The proposed model, fitted using Monolix, accurately captured viral dynamics and provided a strong match with the experimental data. These results indicate that early intervention with antiviral agents combined with immune response enhancement significantly reduces the viral load and promotes the clearance of infected cells. This model serves as a robust tool for predicting HBV progression and optimizing therapeutic strategies, offering potential applications in personalized treatment planning.