FRACTIONAL CALCULUS AND PHYSICS-INFORMED NEURAL NETWORKS FOR HBV DYNAMICS: THEORY, ANALYSIS, AND MACHINE LEARNING VALIDATION

Hepatitis B virus (HBV) remains a major global health threat, causing chronic liver disease, cirrhosis, and hepatocellular carcinoma in millions of people worldwide. Understanding its transmission dynamics is essential for designing effective prevention and control strategies. This study integrates fractional calculus and physics-informed machine learning to analyze HBV transmission dynamics. An eight-compartment fractional-order model (passively immune, susceptible, vaccinated, exposed, acutely infected, chronically infected, treated, recovered) is developed using the Caputo–Fabrizio derivative to capture memory effects. The control reproduction number [Formula: see text] is derived via the next-generation matrix method. Numerical simulations using Newton interpolation for fractional orders [Formula: see text] show that lower orders delay infection peaks by 10–15 years. A Physics-Informed Neural Network (PINN) with three hidden layers (128-64-64) is trained for 3000 epochs on synthetic data with 5% multiplicative noise. The PINN achieves near-perfect agreement with the true ODE solution ([Formula: see text] for most compartments, MAE [Formula: see text] for compartments with larger populations). It also accurately reconstructs fractional derivatives of orders 0.7, 0.8, and 0.9 (MAE [Formula: see text], [Formula: see text] for most compartments). The method is robust to noise, making it suitable for real-world surveillance data. This combined framework provides a mathematically rigorous and computationally efficient tool for evidence-based HBV prevention strategies.