In this study, we utilize the innovative fractal-fractional operator in the Atangana–Baleanu sense to analyze the co-infection dynamics of monkeypox and HIV. Our model integrates key interactions influencing disease transmission and rigorously examines essential mathematical properties. We determine the fundamental reproduction number \((R_0)\) is calculated to assess the potential spread of co-infections and to evaluate the effectiveness of control measures and equilibrium points, delineating the feasible parameter space. Stability analysis is conducted using Banach’s fixed-point theorem and Picard’s successive approximations, supported by Hyers-Ulam stability consistency checks. Additionally, we develop a numerical approach based on the Newton polynomial method to validate our analytical findings. Through comprehensive numerical simulations, we illustrate the intricate effects of fractal and fractional parameters on disease progression. The results provide crucial insights into the impact of control strategies for mitigating monkeypox-HIV co-infection.
