Monkeypox, transmitted primarily through close contact and zoonotic spillover, poses significant public health concerns and economic burdens in affected regions. In order to explore the transmission mechanism of this disease, we construct a dynamic transmission model across risk groups, and simulated different control measures in high-risk (MSM) and low-risk populations. The existence and stability of disease-free and endemic equilibria of the system are analyzed, which are totally determined by the basic reproduction number. Using the MCMC algorithm, we fit the model to mpox case data from the US, Germany, Spain, and the UK. The results indicate that the UK exhibits the highest transmission rate, while the US demonstrates the lowest. Spain and Germany show higher modification parameters for low-risk populations, contrasting with the UK’s minimal value. These model outputs align closely with observed national mpox prevalence rates. Numerical simulations reveal that enhancing awareness among low-risk populations and reducing the modification parameter for individuals with low-risk forces of infection should be prioritized through intervention strategies. Implementing control measures aimed at high-risk groups (MSM), is also crucial in reducing overall infection rates.