The Generalized Euler Method for Analyzing Zoonotic Disease Dynamics in Baboon–Human Populations

This study presents a novel fractional-order mathematical model to investigate zoonotic disease transmission between humans and baboons, incorporating the Generalized Euler Method and highlighting key control strategies such as sterilization, restricted food access, and reduced human–baboon interaction. The model’s structure exhibits an inherent symmetry in the transmission dynamics between baboon and human populations, reflecting balanced interaction patterns. This symmetry is further analyzed through the stability of infection-free and endemic equilibrium points, guided by the basic reproduction number R0. Theoretical analyses confirmed the existence, uniqueness, and boundedness of solutions, while sensitivity analysis identified critical parameters influencing disease spread. Numerical simulations validated the effectiveness of intervention strategies, demonstrating the impact of symmetrical measures on minimizing zoonotic disease risks and promoting balanced population health outcomes. This work contributes to epidemiological modeling by illustrating how symmetry in control interventions can optimize zoonotic disease management.