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Countries restrict the overall extent of international travel and migration to balance the expected costs and benefits of mobility. Given the ever-present threat of new, future pandemics, how should permanent restrictions on mobility respond? A simple theoretical framework predicts that reduced exposure to pre-pandemic international mobility causes slightly slower arrival of the pathogen. A standard epidemiological model predicts no decrease in the harm of the pathogen if travel ceases thereafter and only a slight decrease in the harm (for plausible parameters) if travel does not cease. We test these predictions across four global pandemics in three different centuries: the influenza pandemics that began in 1889, 1918, 1957, and 2009. We find that in all cases, even a draconian 50 percent reduction in pre-pandemic international mobility is associated with 1–2 weeks later arrival and no detectable reduction in final mortality. The case for permanent limits on international mobility to reduce the harm of future pandemics is weak.