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In August 2020, as Texas was coming down from a large summer COVID-19 surge, forecasts suggested that Hurricane Laura was tracking towards 6M residents along the East Texas coastline, threatening to spread COVID-19 across the state and cause pandemic resurgences. To assist local authorities facing the dual-threat, we integrated survey expectations of coastal residents and observed hurricane evacuation rates in a statistical framework that combined with local pandemic conditions predicts how COVID-19 would spread in response to a hurricane. For Hurricane Laura, we estimate that 499,500 [90% Credible Interval (CI): 347,500, 624,000] people evacuated the Texan counties, that no single county accumulated more than 2.5% of hurricane evacuees, and that there were 2,900 [90% CI: 1,700, 5,800] exportations of Covid-19 across the state. In general, reception estimates were concentrated in regions with higher population densities. Nonetheless, higher importation risk is expected in small Districts, with a maximum number of importations of 10 per 10,000 residents in our case study. Overall, we present a flexible and transferable framework that captures spatial heterogeneity and incorporates geographic components for predicting population movement in the wake of a natural disaster. As hurricanes continue to increase in both frequency and strength, our framework can be deployed in response to anticipated hurricane paths to guide disaster preparedness and planning.