The outbreak of COVID-19 disrupts the life of many people in the world. In response to this global pandemic, various institutions across the globe had soon issued their prevention guidelines. Governments in the US had also implemented social distancing policies. However, those policies, which were designed to slow the spread of COVID-19, and its compliance, have varied across the states, which led to spatial and temporal heterogeneity in COVID-19 spread. This paper aims to propose a spatio-temporal model for quantifying compliance with the US COVID-19 mitigation policies at a regional level. To achieve this goal, a specific partial differential equation (PDE) is developed and validated with short-term predictions. The proposed model describes the combined effects of transboundary spread among state clusters in the US and human mobilities on the transmission of COVID-19. The model can help inform policymakers as they decide how to react to future outbreaks.