Mathematical Insights into Zoonotic Disease Spread: Application of the Milstein Method

This study develops a mathematical model to explore zoonotic disease transmission dynamics between baboons and humans in the Al-Baha region. The model incorporates key intervention strategies—sterilization, restricted food access, and reduced human-baboon interactions—to mitigate disease spread. Theoretical analysis establishes the existence, uniqueness, non-negativity, and boundedness of solutions, ensuring biological validity. Stability analysis identifies infection-free and endemic equilibria, with the basic reproduction number \( R_0 \) characterizing disease persistence or eradication. A stochastic version of the model, implemented using the Milstein method, captures the impact of environmental and social variability on disease dynamics. Sensitivity analysis highlights critical parameters influencing transmission dynamics, while numerical simulations emphasize the importance of combining control measures. This comprehensive approach offers actionable insights for effective public health and wildlife management strategies.