  Italy has been one of the first countries timewise strongly impacted by the
COVID-19 pandemic. The adoption of social distancing and heavy lockdown
measures is posing a heavy burden on the population and the economy. The timing
of the measures has crucial policy-making implications. Using publicly
available data for the pandemic progression in Italy, we quantitatively assess
the effect of the intervention time on the pandemic expansion, with a
methodology that combines a generalized
susceptible-exposed-infectious-recovered (SEIR) model together with statistical
learning methods. The modeling shows that the lockdown has strongly deviated
the pandemic trajectory in Italy. However, the difference between the forecasts
and real data up to 20 April 2020 can be explained only by the existence of a
time lag between the actual issuance date and the full effect of the measures.
To understand the relative importance of intervention with respect to other
factors, a thorough uncertainty quantification of the model predictions is
performed. Global sensitivity indices show that the the time of intervention is
4 times more relevant than quarantine, and eight times more important than
intrinsic features of the pandemic such as protection and infection rates. The
relevance of their interactions is also quantified and studied.
