Zoonotic Disease Transmission Between Baboons and Humans in Al-Baha: A Caputo-Fabrizio Fractal-Fractional Order Modeling Study

Baboons in Saudi Arabia’s Al Baha province frequently interact with people, creating crossspecies transmission settings that classical, integer-order epidemic models cannot reproduce. By utilizing the Caputo-Fabrizio fractional operator, we are able to encode history effects via a nonsingular kernel over two hosts with nonlocal memory. Memory strength determines outbreak magnitude, decay rates, and oscillatory patterns across a range of fractional indices. It can precipitate a variety of complex and chaotic transients absent from the integer-order limit. Mathematically, we establish Ulam-Hyers stability for the proposed dynamic, ensuring solution robustness under small perturbations and modelling noise. The resulting methodology offers a principled tool for designing public-health actions and wildlife management policies in regions with sustained human-wildlife interfaces.