Mobility restriction is a crucial measure to control the transmission of the COVID-19. Research has shown that effective distance measured by the number of travelers instead of physical distance can capture and predict the transmission of the deadly virus. However, these efforts have been limited mainly to a single source of disease. Also, they have not been tested on finer spatial scales. Based on prior work of effective distances on the country level, we propose the multiple-source effective distance, a metric that captures the distance for the virus to propagate through the mobility network on the county level in the U.S. Then, we estimate how the change in the number of sources impacts the global mobility rate. Based on the findings, a new method is proposed to locate sources and estimate the arrival time of the virus. The new metric outperforms the original single-source effective distance in predicting the arrival time. Last, we select two potential sources and quantify the arrival time delay caused by the national emergency declaration. In doing so, we provide quantitative answers on the effectiveness of the national emergency declaration.
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