  Without a vaccine, the fight against the spreading of the coronavirus has
focused on maintaining physical distance. To study the impact of such measures
on inter-municipality traffic, we analyze a mobile dataset with the daily flow
of people in Portugal in March and April 2020. We find that the reduction in
inter-municipality traffic depends strongly on its initial outflow. In
municipalities where the mobility is low, the outflow reduced by $10-20\%$ and
this decrease was independent of the population size. Whereas, for
municipalities of high mobility, the reduction was a monotonic increasing
function of the population size and it even exceeded $60\%$ for the largest
municipalities. As a consequence of such heterogeneities, there were
significant structural changes on the most probable paths for the spreading of
the virus, which must be considered when modeling the impact of control
measures.
