Fractional-Order SEIQRDC Epidemic Model with Memory Effects, Confinement Strategies, and Lévy Noise-Driven Stochastic Dynamics

Existing epidemic models typically capture either memory effects via fractional calculus or stochasticity via Gaussian noise, but fail to jointly address the heavy-tailed extremes characteristic of superspreader events and abrupt policy shifts. This paper addresses this gap by introducing, to the best of our knowledge, a fractional-order SEIQRDC epidemic model driven by Lévy noise ([Formula: see text] = 1.5), unifying memory-dependent dynamics with heavy-tailed fluctuations within a seven-compartment framework that explicitly models confinement strategies. Numerical simulations reveal three key advances that distinguish this work from existing formulations. First, under the adopted effective-rate formulation, the model yields a timedependent reproduction indicator alongside the threshold quantity [Formula: see text], with [Formula: see text] [Formula: see text] 0.3815 for [Formula: see text] = 0.9, providing a dynamic perspective on transmission potential. Second, varying the fractional order [Formula: see text] [0.7, 1.0] uncovers a memory-speed trade-off: stronger memory (lower [Formula: see text]) reduces peak infections by up to 38% but prolongs epidemic duration by 2–3 weeks, offering quantitative guidance for intervention timing. Third, Lévy jumps generate biologically realistic sudden surges (up to 12% compartmental shifts in under 5 days) while also highlighting the need for biologically constrained stochastic formulations in cumulative compartments. In the numerical implementation used here, non-negativity is enforced computationally to preserve epidemiological realism. The confined susceptible compartment ([Formula: see text]) captures the protective effect of non-pharmaceutical interventions, demonstrating that early confinement rapidly shields a large fraction of the population. A numerical scheme combining a discrete fractional update with a jump-perturbed stochastic update provides a useful framework for exploring both gradual containment strategies and abrupt intervention effects under uncertainty. This framework advances epidemic modeling by simultaneously addressing memory, extreme events, and confinement strategies within a unified stochastic fractional formulation.