  Travel restrictions have often been used as a measure to combat the spread of
disease -- in particular, they have been extensively applied in 2020 against
coronavirus disease 2019 (COVID-19). How to best restrict travel, however, is
unclear. Most studies and policies simply constrain the distance r individuals
may travel from their home or neighbourhood. However, the epidemic risk is
related not only to distance travelled, but also to frequency of contacts,
which is proxied by the frequency f with which individuals revisit locations
over a given reference period. Inspired by recent literature that uncovers a
clear universality pattern on how r and f interact in routine human mobility,
this paper addresses the following question: does this universal relation
between r and f carry over to epidemic spreading, so that the risk associated
with human movement can be modeled by a single, unifying variable r * f? To
answer this question, we use two large-scale datasets of individual human
mobility to simulate disease spread. Results show that a universal relation
between r and f indeed exists in the context of epidemic spread: in both of the
datasets, the final size and the spatial distribution of the infected
population depends on the product r * f more directly than on the individual
values of r and f. The important implication here is that restricting r (where
you can go), but not f (how frequently), could be unproductive: high frequency
trips to nearby locations can be as dangerous for disease spread as low
frequency trips to distant locations. This counter-intuitive discovery could
explain the modest effectiveness of distance-based travel restrictions and
could inform future policies on COVID-19 and other epidemics.
