@article{Alhazmi2025, 
author = {Muflih Alhazmi and Safa M. Mirgani and Abdullah Alahmari and Sayed Saber},
title = {Hybrid multi-step fractional numerical schemes for human-wildlife zoonotic disease dynamics},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {21126-21158},
keywords = {fractional derivatives, nonlinear equations, simulation, numerical results, iterative method, zoonotic disease},
url = {https://www.sciopen.com/article/10.3934/math.2025944},
doi = {10.3934/math.2025944},
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.}
}