…two opposing forces constitute the first-order determinants of total infections at any point in time. On one hand, the longer a travel ban lasts, the less time community transmission exists in the rural sink. Ceteris paribus, this will decrease rural infections. On the other hand, the longer the restrictions remain, the longer migrants are contained within a hotspot where infection rates are rapidly increasing. Consequently, the probability that migrants are infected with Covid-19 rises over time until the city achieves herd immunity, in turn increasing the rate at which they seed the rural sink with infections once the ban is lifted. This drives up cumulative cases at any future date.
In some cases, for travel bans to work they have to be very long. That is from a new paper by Fiona Burlig, Anant Sudarshan, Garrison Schlauch, who also provide evidence from India, and also from cross-country evidence, to support their analysis.