Changes in human activities after the introduction of tiers

To assess the impact of tiers on human activities, we used mobility data to calibrate a linear mixed model for each of the location categories in the Google reports⁸. The LMMs are of the form:

where

M_p,l represents the mobility value of a given location category (i.e., the change in the number of visitors in non-residential locations, or the change in the time spent at home, normalized to the pre-pandemic values) in each of the 107 Italian provinces (p), averaged over the days in which a given tier l was enforced;

Lpl is a binary variable set to 1 when the considered value M_p,l belongs to a province with tier l, and 0 otherwise;

β₀,β₁,β₂ and β₃ and are model parameters, with β₀ representing the mean mobility across Italian provinces during the period October 14–November 5 (i.e., before the tier system);

a_r and b_r,p are random effects, assumed to be normally distributed. a_r allows random deviations from the mean among regions; b_r,p allows random deviations from the mean regional mobility among provinces within a region;

ε_p,T is random noise assumed to be normally distributed.