An application of Newton’s interpolation polynomials to the zoonotic disease transmission between humans and baboons system based on a time-fractal fractional derivative with a power-law kernel

Abstract

This study introduces a novel mathematical model to explore zoonotic disease transmission between humans and baboons. By utilizing fractal-fractional derivatives with a power-law kernel, the model captures time-dependent dynamics that traditional approaches cannot. A Hyers–Ulam stability analysis is used to assess the robustness of the model under small perturbations, demonstrating the existence and uniqueness of the solution. Control strategies such as sterilization, food restrictions, and human interaction are evaluated numerically. Key findings reveal the significant influence of fractal-fractional parameters on disease progression and control measures. Simulations demonstrate the model’s ability to represent real-world dynamics, providing valuable insights into effective interventions, including sterilization, food restrictions, and reduced human–baboon interactions. This framework offers a comprehensive tool for understanding and mitigating zoonotic disease risks.