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 $({\beta }_h)$, the human recovery rate $({\gamma }_h)$, 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.