Artificial Intelligence-Driven Inverse Identification of Fractional Epidemic Models with Generalized Incidence Functions

We present an identifiability-aware inverse-learning workflow for a dimensionally consistent Caputo fractional-order SEAIHRD epidemic model incorporating generalized incidence, asymptomatic transmission, hospitalization dynamics, waning immunity, and an ordinary cumulative-death balance. For the autonomous system, we establish positivity, forward invariance, global well-posedness, threshold and stability results, endemic-equilibrium existence and uniqueness, and sensitivity properties. To infer unobserved dynamics, we combine practical-identifiability screening, multistart fractional calibration, profile likelihood, bootstrap analysis, and constrained PINN state reconstruction. In the matched-information synthetic inverse benchmark, conventional fractional calibration outperforms direct joint-PINN parameter fitting for retained-parameter recovery and hidden-state error: hidden-state RMSE is 0.00142 versus 0.161 on clean data, 0.0203 versus 0.142 at 2% noise, and 0.0207 versus 0.139 at 5% noise. In the separate fixed-parameter reconstruction task, adding the governing-equation residual reduces mean hidden-state RMSE by 49–51% relative to the matched no-dynamics-residual ablation, although the resulting absolute mean hidden-state RMSE remains 0.129–0.144 and susceptible-state RMSE remains 0.336–0.348. In Italian COVID-19 data, a stock-consistent observation model yields admissible reconstructions, but the real-data scalar inverse problem is practically non-identifiable; the reconstructed latent states are a model-conditioned decomposition of the reported active-positive stock under a unit reporting factor, not a census of unreported community infection. Rolling-origin constant-endpoint-β forecasts underperform simple baselines on average. Adding the governing-equation residual, therefore, regularizes latent-state reconstruction relative to the matched constrained neural ablation under the tested design, without guaranteeing unique parameter identification or forecast superiority.