A fractional ABC model for hepatitisB virus transmission with forecasting of epidemic trends using neural networks

This paper develops a fractional-order HBV epidemic model using the Atangana-Baleanu-Caputo (ABC) fractional derivative with a nonsingular Mittag-Leffler kernel to capture memory-dependent epidemic dynamics associated with chronic HBV progression. The model incorporates vaccinated, susceptible, exposed, infected, and recovered compartments together with vaccination, waning immunity, recovery, and disease-induced mortality. The basic reproduction number [Formula: see text] and the disease-free equilibrium are derived, and local as well as global stability analyses are performed. Sensitivity analysis identifies the effective contact rate as the strongest positive contributor to disease transmission, whereas the recovery rate has the strongest negative influence on [Formula: see text]. An ABC-adapted predictor-corrector numerical framework based on the fde12 methodology is implemented to simulate the fractional HBV system. Numerical results show that decreasing the fractional order strengthens memory effects, slows epidemic progression, and prolongs transient dynamics. In addition, a feedforward artificial neural network (ANN) trained on simulation-generated trajectories is employed to investigate surrogate forecasting capability for infected and recovered populations. Using a temporally separated training and testing strategy, the ANN accurately approximated the simulated infected and recovered trajectories, demonstrating the feasibility of surrogate forecasting for ABC-fractional epidemic dynamics. The results highlight the usefulness of nonsingular fractional operators for modelling chronic infectious diseases and demonstrate the potential of combining mechanistic fractional models with machine-learning-based surrogate forecasting frameworks.