Figure 4

Associating mortality to local mobility and positivity. (a) Local mobility curves (Google’s “Groceries & pharmacy”) and positivity curves (regularized ratios of new cases to number of tests performed) in the 20 Italian regions. Curves are smoothed with splines, with degree of smoothing selected by generalized cross-validation, and shifted based on probKMA run on the MAX mortality curves with \(K=2\); time is marked as a day number representing the region-specific time of the epidemic unfolding, and corresponds to actual time (starting on February 16 and ending on April 30) only for regions with no shifts, e.g., Lombardia. Vertical lines show the days corresponding to the nationwide lock-down (March 9) and the suspension of all nonessential production activities (March 23) without shifts, stars on the curves mark the lock-down after the region specific shifts. The example regions of Fig. 1(a) are highlighted in color. (b) Estimated effect surfaces from the joint function-on-function regression of MAX mortality on local mobility and positivity shown in 3D and as contour plots (March 9, without shift, is again marked on both). Early and mid-period local mobility levels are strong positive predictors of mortality at its peak. Positivity has similar but much weaker predictive signals, likely because the effects are subsumed by mobility. Late local mobility has a negative association with mortality at its peak (mobility resumed faster in regions with milder epidemics), and late positivity a strong positive one (positivity remained elevated in regions with worse epidemics). The regression captures a large share of the variability in mortality curves (in-sample \(R^2=0.90\), LOO-CV \(R^2=0.52\)), with substantial and comparable contributions of the two predictors (partial \(R^2\)s \(=0.62, 0.53\)).