Travel restrictions during pandemics: A useful strategy?

Though carrying considerable economic and societal costs, restricting individuals’ traveling freedom appears as a logical way to curb the spreading of an epidemic. However, whether, under what conditions, and to what extent travel restrictions actually exert a mitigating effect on epidemic spreading are poorly understood issues. Recent studies have actually suggested the opposite, i.e., that allowing some movements can hinder the propagation of a disease. Here, we explore this topic by modeling the spreading of a generic contagious disease where susceptible, infected, or recovered point-wise individuals are uncorrelated random-walkers evolving within a space comprising two equally sized separated compartments. We evaluate the spreading process under different separation conditions between the two spatial compartments and a forced relocation schedule. Our results confirm that, under certain conditions, allowing individuals to move from regions of high to low infection rates may turn out to have a positive effect on aggregate; such positive effect is nevertheless reduced if a directional flow is allowed. This highlights the importance of considering travel restriction policies alternative to classical ones. At the beginning of any major pandemic, i.e., when cases are still restricted to one or few countries, governments worldwide try to prevent the disease from entering their territories by limiting international travels. The same strategy is also applied at a more local scale, e.g., by restricting travels between regions, also after the disease has reached all of them. It is nevertheless easy to see that an individual living in a region with a high infection rate would benefit from moving to a lower rate one; the question then becomes whether and under which conditions are those restrictions really beneficial. Using a simple random-walker model, we here show that travel restrictions are beneficial for regions with low infection rates, as indeed new imported cases are limited; nevertheless, this goes against the interest of the system as a whole, as free movements can reduce the total number of cases.This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 851255). M.Z. acknowledges the Spanish State Research Agency through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (No. MDM-2017-0711)