AI-DRIVEN ANALYSIS OF FRACTAL SCALING IN FRACTIONAL-ORDER NOROVIRUS TRANSMISSION MODELS WITH L-BFGS-B PARAMETER CALIBRATION

Norovirus is a leading cause of acute gastroenteritis worldwide, characterized by high transmissibility, environmental persistence, and limited lasting immunity. We propose and analyze a fractional-order norovirus transmission model with vaccination, environmental contamination, and multiple infection stages including pathogen. The model is constructed with the Atangana–Baleanu fractional derivative to capture memory effects in epidemiological dynamics. We establish the well-posedness of the system: positivity, boundedness, and invariance of solutions are proved, and existence and uniqueness of solutions are analyzed via fixed-point theory. The disease-free equilibrium is computed and the basic reproduction number [Formula: see text] is derived using the next-generation matrix approach, followed by a sensitivity analysis (PRCC) to identify key parameters. A numerical scheme based on Lagrange interpolation is developed, and Ulam–Hyers stability is verified. Synthetic data are generated for fractional orders [Formula: see text] and the integer case [Formula: see text]. The unknown transmission parameters [Formula: see text] (from quarantine) and [Formula: see text] (recovery rate from quarantine) are estimated by nonlinear least squares (L-BFGS-B optimization) using 80% of the data for training and the remaining 20% for testing, with a detailed algorithm and flowchart provided. The fitted model is analyzed through RMSE, MAE, and [Formula: see text] for all eight compartments. Results show that for [Formula: see text] the model achieves near-perfect agreement with test data ([Formula: see text]), while for [Formula: see text] and [Formula: see text] parameter estimation shows disturbance, leading to negative [Formula: see text] values for some compartments. These findings demonstrate that fractional orders below [Formula: see text] provide a more robust description of norovirus dynamics and facilitate parameter recovery. The study highlights the value of combining fractional calculus with rigorous theoretical analysis and modern optimization for epidemiological modelling.