Fractional Epidemic Dynamics With Memory: Rigorous Analysis, Data‐Constrained Learning, and Physics‐Informed Forecasting

This paper investigates a fractional‐order susceptible–exposed–symptomatic infectious–asymptomatic infectious–treated–recovered (SEIATR) epidemic model in the Caputo sense. The study establishes well‐posedness, derives the basic reproduction number, and analyzes equilibrium stability. An L1 discretization and a physics‐informed neural network are then used for simulation, surveillance‐informed reconstruction, and short‐horizon forecasting. The results show that memory mainly affects epidemic timing, wave broadening, and persistence, whereas the learning framework delivers accurate reconstruction and competitive forecasting performance.