https://www.aimspress.com/journal/Math AIMS Mathematics, 10(9): 21126–21158. DOI: 10.3934/math.2025944 Received: 12 June 2025 Revised: 21 July 2025 Accepted: 24 July 2025 Published: 15 September 2025 Research article Hybrid multi-step fractional numerical schemes for human-wildlife zoonotic disease dynamics Muflih Alhazmi 1, * , Safa M. Mirgani 2 , Abdullah Alahmari 3 and Sayed Saber 4,5 1 Mathematics Department, Faculty of Science, Northern Border University, Arar, Saudi Arabia 2 Imam Mohammad Ibn Saud Islamic University (IMSIU), College of Science Department of Mathematics and Statistics, Riyadh, Saudi Arabia 3 Department of Mathematical, Faculty of Sciences, Umm Al-Qura University, Saudi Arabia 4 Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha, Saudi Arabia 5 Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Egypt * Correspondence: Email: Muflih.alhazmi@nbu.edu.sa. Abstract: In this study, the transmission dynamics of zoonotic diseases between baboons and humans were explored by examining increased interactions between humans and wild animals. We established the model’s well-posedness through proofs of existence, uniqueness, non-negativity, and boundedness of solutions. Stability and sensitivity analyses identified key parameters affecting disease dynamics, particularly the baboon-to-human transmission rate (β h ), the human recovery rate (γ h ), and the human- side contact control parameter (H i ). The basic reproduction number (R 0 ) governed disease outcomes: If R 0 < 1, the disease died out and the infection-free equilibrium was globally asymptotically stable; if R 0 > 1, a unique endemic equilibrium emerged and was locally asymptotically stable, indicating the potential for disease persistence. Numerical simulations were conducted using the Multi-Step Generalized Differential Transform Method and the Adams-Bashforth-Moulton scheme, confirming the model’s biological relevance. Our results indicated that sterilization reduced infected baboons by up to 40%, while food access restrictions lowered human infections by approximately 25%. By leveraging fractional calculus and advanced numerical methods, this study provides a robust framework for modeling zoonotic diseases and offers actionable insights for public health and wildlife management. Keywords: fractional derivatives; nonlinear equations; simulation; numerical results; iterative method; zoonotic disease Mathematics Subject Classification: 34A08, 34L99, 92D30