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Policymakers everywhere are working to determine the set of restrictions that will effectively contain the spread of COVID-19 without excessively stifling economic activity. We show that publicly available data on human mobility -- collected by Google, Facebook, and other providers -- can be used to evaluate the effectiveness of non-pharmaceutical interventions and forecast the spread of COVID-19. This approach relies on simple and transparent statistical models, and involves minimal assumptions about disease dynamics. We demonstrate the effectiveness of this approach using local and regional data from China, France, Italy, South Korea, and the United States, as well as national data from 80 countries around the world.