In this paper, we investigate a deterministic mathematical model of Marburg–Monkeypox virus co-infection transmission under the Caputo fractional-order derivative. We discussed the dynamics behavior of the model and carried out qualitative and quantitative analysis, including the positivity–boundedness of solution, and the basic reproduction number ℜo. In addition, the Banach and Schauder-type fixed point theorem is utilized to explore the existence–uniqueness of the solution in the suggested model and the proposed model stability under the Ulam–Hyers condition is demonstrated. In numerical simulation, the Predictor–Corrector method is used to determine the numerical solutions. According to the numerical result, increasing the rate of quarantine and detecting unknown Marburg virus, will be the most effective control intervention to reduce Marburg and Monkeypox virus transmission in the population.