BACKGROUND: Monkeypox (Mpox) is an  emerging infectious disease caused by the Mpox virus (MPX Virus). The outbreak of Mpox epidemic has caused global panic and is now a public health incident. Various approaches have been proposed in the recent literature to study and analyze the epidemiological dynamics of this infection and effective prevention and control measures. Using mathematical model to understand the transmission dynamics and control strategy is a useful way to understand the prevention of Mpox. METHODS: A new compartment model is established to examine the effectiveness of vaccine on Mpox based on previous studies. Nonlinear least squares fitting is used for model's parameter estimation. The impact of a series of preventive and control measures on the epidemic control is explored with optimal control theory in conjunction with the official data released by the authorities. RESULTS: Firstly, a stability analysis of the developed model was carried out to show that, under certain circumstances, its equilibrium is both locally and globally stable. Secondly, based on the reported cases of Mpox infection in the United States between 2022 and 2023, the model's optimal parameter values were obtained. A sensitivity analysis of the model parameters was then conducted to identify the key parameters that affect the development of Mpox epidemics in the United States. Lastly, the comparison of control effects under various control strategies showed that implementing the all suggested four control measures at the same time was the most effective way to curb the development of monkeypox epidemic in the United States. CONCLUSIONS: This study has theoretical significance for understanding and controlling Mpox virus transmission.