Mobility data

Mobility data, M(t), with one data point per day, t, were downloaded from Apple repository on August 31, 2020 (Data ref: Apple, 2020). The Apple dataset reports the daily volume of directions requested from Apple maps on mobile cellphones for driving, walking, or using transit (public transportation) in a specified region. The amount of requests per day is reported as the percentage with respect to a benchmark (100%) set on January 13, 2020. For extracting features that characterize the lockdown, we focused our analysis on the lockdown period (January 13 to May 10, corresponding to 119 data points). Due to the high similarity between “walking” and “driving” data during the lockdown period (average correlation across countries r ² = 0.91, SD = 0.07, max P value = 10⁻¹²⁹) and since the “transit” data are incomplete, all analyses were applied using the “driving” data only.

To fit M^(t) to the mobility data M(t) during the lockdown period and to infer the values of the parameters for every country, we used the Levenberg–Marquardt optimization algorithm from the SciPy module (Levenberg, 1944; Marquardt, 1963; Virtanen et al, 2020). According to the parameters inferred from M^(t), we computed seven features to characterize the mobility trend in a country, as follows: (i) t′, Social distancing start time; and (ii) t″, Minimal mobility time point, corresponding to the times before and after the mobility drop.  These points are defined as time 95% and 5% of the drop, parameterized by L, and t ⁰ is the middle time point between them (see Fig 1A). Thus, M^(t′)=0.95L+b and M^(t″)=0.05L+b Then,

Similarly, t″=t0+ln19k (note that k is negative); (iii) Drop duration, the time difference t″−t′=2ln19k; (iv) Lockdown release day t ¹; (v) Lockdown strictness LL+M^(t1)×100, such that M^(t1) is the function value at the release day; (vi) Lockdown duration t ¹ –t″; (vii) Lockdown release rate a (the slope of the linear function).