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(1) Background: Human mobility between geographic units is an important way in which COVID-19 is spread across regions. Due to the pressure of epidemic control and economic recovery, states in the United States have adopted different policies for mobility limitations. Assessing the impact of these policies on the spatiotemporal interaction of COVID-19 transmission among counties in each state is critical to formulating epidemic policies. (2) Methods: We utilized Moran's I index and K-means clustering to investigate the time-varying spatial autocorrelation effect of 49 states (excluding the District of Colombia) with daily new cases at the county level from 22 January 2020 to 20 August 2020. Based on the dynamic spatial lag model (SLM) and the SIR model with unreported infection rate (SIRu), the integrated SLM-SIRu model was constructed to estimate the inter-county spatiotemporal interaction coefficient of daily new cases in each state, which was further explored by Pearson correlation test and stepwise OLS regression with socioeconomic factors. (3) Results: The K-means clustering divided the time-varying spatial autocorrelation curves of the 49 states into four types: continuous increasing, fluctuating increasing, weak positive, and weak negative. The Pearson correlation analysis showed that the spatiotemporal interaction coefficients in each state estimated by SLM-SIRu were significantly positively correlated with the variables of median age, population density, and proportions of international immigrants and highly educated population, but negatively correlated with the birth rate. Further stepwise OLS regression retained only three positive correlated variables: poverty rate, population density, and highly educated population proportion. (4) Conclusions: This result suggests that various state policies in the U.S. have imposed different impacts on COVID-19 transmission among counties. All states should provide more protection and support for the low-income population; high-density populated states need to strengthen regional mobility restrictions; and the highly educated population should reduce unnecessary regional movement and strengthen self-protection. [ABSTRACT FROM AUTHOR]