Nonlinear SEIS Epidemic Dynamics with Fractional-Order Time: Analytical and Numerical Results

Abstract

This study investigates a novel SEIS epidemic model that incorporates fractional-order derivatives to account for the memory effects of the disease spread. The Caputo derivative is specifically employed. Furthermore, the model considers the influence of behavioral changes in susceptible individuals by incorporating a general non-linear function that depends on their population size. Leveraging recent advancements in fractional differential equations theory, we establish the existence of solutions and analyze the critical conditions for the system’s steady states to achieve global asymptotic stability. Finally, the validity and applicability of the theoretical model are corroborated through numerical simulations using real-world data on the prevalence of Pneumococcus.