The recent resurgence of Monkeypox (Mpox) necessitates the development of effective control strategies to manage its transmission. This study presents a comprehensive approach to modeling and controlling Mpox dynamics by incorporating human mobility into a deterministic framework. We begin by constructing a detailed model that integrates human mobility, providing a realistic depiction of the disease’s spread. Subsequently, we analyze the disease-free equilibrium and calculate the basic reproduction number, R0. The study also formulates an optimal control problem, identifying the most effective strategies for mitigating Mpox spread through mobility, treatment, and animal control. We perform parameter estimation and model fitting to ensure the model’s accuracy and relevance to real-world data. A global sensitivity analysis using the Partial Rank Correlation Coefficient (PRCC) and hypercube sampling determines which parameters most significantly influence R0. Numerical simulations show that a complete lockdown prevents transmission, whereas limiting all movement delays outbreaks but extends their length. Internal mobility control outperforms unconstrained movement, considerably reducing infection peaks. Treatment-only approaches reduce cases by about 50%, whereas animal control prevents outbreaks by lowering human exposure. The most effective technique involves movement restrictions, medication, and animal management, reducing peak infections by more than 90%. Sensitivity analysis demonstrates that transmission rates and mobility patterns have the most significant influence on disease spread. Our findings provide a robust framework for controlling Mpox transmission, focusing on the critical role of human mobility and providing practical information for public health interventions. © The Author(s) under exclusive licence to Sociedade Brasileira de Física 2025.