  In 2020, countries affected by the COVID-19 pandemic implemented various
non-pharmaceutical interventions to contrast the spread of the virus and its
impact on their healthcare systems and economies. Using Italian data at
different geographic scales, we investigate the relationship between human
mobility, which subsumes many facets of the population's response to the
changing situation, and the spread of COVID-19. Leveraging mobile phone data
from February through September 2020, we find a striking relationship between
the decrease in mobility flows and the net reproduction number. We find that
the time needed to switch off mobility and bring the net reproduction number
below the critical threshold of 1 is about one week. Moreover, we observe a
strong relationship between the number of days spent above such threshold
before the lockdown-induced drop in mobility flows and the total number of
infections per 100k inhabitants. Estimating the statistical effect of mobility
flows on the net reproduction number over time, we document a 2-week lag
positive association, strong in March and April, and weaker but still
significant in June. Our study demonstrates the value of big mobility data to
monitor the epidemic and inform control interventions during its unfolding.
