Fractional Bi-Susceptible Approach to COVID-19 Dynamics with Sensitivity and Optimal Control Analysis

This study introduces a nonlinear fractional bi-susceptible model for COVID-19 using the Atangana–Baleanu derivative in Caputo sense (ABC). The fractional framework captures nonlocal effects and temporal decay, offering a realistic presentation of persistent infection cycles and delayed recovery. Within this setting, we investigate multiple transmission modes, determine the major risk factors, and analyze the long-term dynamics of the disease. Analytical results are obtained at equilibrium states, and fundamental properties of the model are validated. Numerical simulations based on the Toufik–Atangana method further endorse the theoretical results and emphasize the effectiveness of the ABC derivative. Bifurcation analysis illustrates that adjusting time-invariant treatment and awareness efforts can accelerate pandemic control. Sensitivity analysis identifies the most significant parameters, which are used to construct an optimal control problem to determine effective disease control strategies. The numerical results reveal that the proposed control interventions minimize both infection levels and associated costs. Overall, this research work demonstrates the modeling strength of the ABC derivative by integrating fractional calculus, bifurcation theory, and optimal control for efficient epidemic management.