FRACTAL–FRACTIONAL MODEL OF ZOONOTIC DISEASE TRANSMISSION BETWEEN HUMANS AND BABOONS IN THE AL-BAHA REGION WITH APPLICATIONS TO DYNAMICS, TRANSPORT PROCESSES, AND HYERS–ULAM STABILITY ANALYSIS

This paper presents a mathematical model for zoonotic disease transmission between baboons and humans in the Al-Baha region using a fractal–fractional derivative approach. The model incorporates compartments for susceptible, infected, and recovered populations of both species. The Atangana–Baleanu fractal–fractional derivative captures memory effects and interactions between humans and baboons. The existence and uniqueness of the solution are demonstrated through fixed-point theorems, and Hyers–Ulam stability analysis is applied to assess the robustness of the model under small perturbations. Numerical simulations evaluate various control strategies, including sterilization, food restrictions, and limiting human interaction. They reveal the critical role of managing wildlife–human contact in reducing disease transmission. The Hyers–Ulam stability confirms that small deviations in initial conditions or parameter values do not significantly alter the long-term behavior of the system, ensuring the reliability of the model’s predictions. This research not only models zoonotic disease transmission, but also explores the broader implications of fractal–fractional derivatives in dynamics and transport processes, offering insights into memory-driven phenomena across various fields. Results highlight the importance of integrated control measures in mitigating zoonotic disease risks.