Modeling Pandemic Dynamics via Fuzzy Fractional SEIQR Framework with ABC Derivatives: Qualitative Analysis and Computational Approaches

Epidemic modeling plays a crucial role in understanding disease transmission and informing public health strategies. This study presents a fractional Susceptible-Exposed-Infected-Quarantined-Recovered (SEIQR) model incorporating Atangana–Baleanu-Caputo (ABC) fractional derivatives to capture memory effects in disease dynamics. The model extends classical ordinary differential equation-based frameworks by integrating a fractional approach, enhancing its applicability to real-world epidemic scenarios. A key feature of our model is the inclusion of mortality rates across all disease compartments, providing a refined representation of influenza-like infections with pandemic potential. We conduct a detailed stability analysis to assess equilibrium states and derive conditions for disease control. Numerical simulations further validate the theoretical findings, offering insights into epidemic progression and intervention strategies. Our results highlight the significance of fractional calculus in epidemiological modeling and its potential to improve predictive accuracy for infectious disease outbreaks.