Dual memory effects and epidemic thresholds in a fractional-order SEIR model

This study develops a fractional-order SEIR model incorporating memory effects through two distinct indices: infectivity memory (1−α1) for exposed individuals and recovery memory (1−α2) for infected individuals. We establish a comprehensive theoretical framework in which the basic reproduction number R0 serves as a sharp threshold for global dynamics: when R0<1, the disease-free equilibrium (DFE) is globally asymptotically stable, whereas when R0>1, a unique endemic equilibrium (EE) becomes globally asymptotically stable. Through sensitivity analysis, we quantify how R0 and equilibrium states respond to variations in memory indices. Numerical simulations across four epidemiological scenarios reveal dual roles of memory effects: as dynamic modulators that reshape transmission trajectories, and as strategic regulators that define scenario-specific control patterns. These include synergistic suppression through coordinated memory reduction in favorable conditions, and competitive modulation requiring balanced memory adjustment in high-transmission settings. Our findings demonstrate that memory indices provide a mathematically-guided framework for precision public health, enabling tailored interventions that adapt to specific transmission-recovery patterns.