Zoonotic diseases, which are transmitted between animals and humans, pose significant public health challenges, especially in regions with high human-wildlife interactions. This study presents a novel fractional-order mathematical model to analyze the transmission dynamics of zoonotic diseases between baboons and humans in the Al-Baha region. The model incorporates the Atangana-Baleanu fractional derivative to account for memory effects and spatial heterogeneity, offering a more realistic representation of disease spread. The fractional Euler method is employed for numerical simulations, enabling accurate predictions of infection trends under various fractional orders. Stability analysis, conducted via the Banach fixed-point theorem and Picard iterative method, confirms the model's robustness, while Hyers-Ulam stability ensures its reliability. Additionally, control strategies, including sterilization, food access restriction, and human interaction reduction, are integrated into the model to assess their effectiveness in disease mitigation. Simulation results highlight the impact of fractional-rder dynamics on disease persistence, showing that lower fractional orders correspond to prolonged infections due to memory effects. These findings underscore the significance of fractional calculus in epidemiological modeling and provide valuable insights for designing effective zoonotic disease control strategies.
Keywords: Fractional Derivatives; Iterative Method; Lyapunov Functions; Stability; Time Varying Control System.
© 2025. The Author(s).