This study develops a mathematical model of Mpox transmission that combines stratified susceptibility (low-risk and high-risk groups) with vaccinated and asymptomatically infected compartments. The analysis of the model begins with examining the well-posedness, boundedness, and nonnegativity conditions for the solutions. The local stabilities of the equilibria are examined through the Jacobian matrix and phase plane analysis, while the global stabilities are provided through Lyapunov functions. The estimated parameters are verified using epidemiological data on Mpox cases in the United States, with an MAPE of 2.20% and R0>1, indicating that Mpox remains endemic. Sensitivity analysis indicates that the contact rate with symptomatic infected individuals, along with the vaccination rate, is the most influential parameter affecting the basic reproduction number of the human population. This highlights the critical role of reducing direct transmission and increasing immunization coverage in controlling disease spread. To address these factors, three control measures—preventive intervention, supportive treatment, and reduction of contact with infected rodents—are systematically examined within an optimal control framework based on Pontryagin's principle. Furthermore, numerical simulations are conducted to demonstrate the dynamic behavior of the infected compartments under various individual and combined control strategies, providing insight into their effectiveness over time. In addition, cost-effectiveness analyses are performed using the Average Cost-Effectiveness Ratio and Incremental Cost-Effectiveness Ratio methods. The results clearly indicate that the integrated implementation of all three control measures yields the most efficient and economically sustainable strategy for mitigating and ultimately suppressing Mpox transmission. © 2026 by the authors. This work is licensed under a Creative Commons Attribution 4.0 (CC BY) International License. The authors retain ownership of the copyright for their article, but they allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in MMNSA, so long as the original authors and source are credited. To see the complete license contents, please visit (http://creativecommons.org/licenses/by/4.0/).