Unveiling Asymptomatic Transmission: Analytical and Stability Insights of a Fractional-Order COVID-19 Model

In this paper, we present a fractional-order SAIP epidemic model that incorporates asymptomatic transmission to jointly examine infection pathways and the influence of long-term memory effects. The Caputo fractional derivative is employed to capture the memory and hereditary characteristics intrinsic to real-world infectious disease dynamics, providing an alternative framework to traditional integer-order approaches. We establish key mathematical properties, including the positivity and boundedness of solutions, and derive the basic reproduction number. $R_0$to determine thresholds for disease extinction or persistence. Both local and global stability analyses of the disease-free and endemic equilibria are conducted to clarify the conditions required for outbreak control. To address the complexities introduced by the fractional structure, we adapt the Laplace Adomian Decomposition Method (LADM) and demonstrate its effectiveness through detailed numerical simulations. The results show that variations in the fractional order affect epidemic trajectories, altering peak infection levels and duration, and thus emphasize the important role of memory effects in disease propagation.