## 3 Results
### Considering the Impact of Restriction Measures on Mobility by Using the Mobility Index  
The records left by the mobile phones of the users (1.4 million users of the Telefonica--Motivstar company) at each antenna when they move inside or to/from the commune are used to build the mobility index of the commune. Using this index as a proxy for human mobility in the commune, we estimated the effects of restriction measures on mobility taken at different dates during the pandemic.  
Figure 6 shows the time series for the mobility index in the observation time period from 27 February 2020 to 5 November 2020 for a sample of 16 communes of the MR (the choice of a sample of size 16 is only to obtain a better visualization, and the analysis is done with all the communes of the MR). The figure also includes the dates that correspond to the most important confinement measures taken in this time interval. The numbers in the figure indicate the dates of the main confinement events (details can be found in Appendix A).  
The mobility index, as shown in Figure 6, makes it possible to capture the impacts on mobility caused by the application of successive confinement measures and their respective lifting at some later time. It is important to highlight the appreciable effect in the reduction of mobility produced by the closure of schools and later, to a much lesser extent, by the different dynamic quarantines enforced on the communes in the first days of the pandemic.  
As of 15 May 2020, a total quarantine was declared for most communes in the MR. In the first days of implementation of this restriction measure, as can be seen in Figure 6, a slight decrease in mobility was recorded in all communes. However, mobility was increasing steadily until reaching the same levels as before the application of quarantine, showing signs of \"fatigue\" in complying with this restriction measure over time. With the gradual exit of the communes from quarantine, a very abrupt increase in mobility is observed.  
Another aspect to highlight is the strong positive correlation found in the mobility index values of all communes of the MR, as is shown in Figure 7. This is a very interesting  
Figure 6: Time series of the mobility index for a sample of 16 MR communes in the period between 27 February 2020 and 5 November 2020. The dates corresponding to the most important confinement measures are highlighted.  
finding and deserves further study; however, it is outside the scope of this work. In practice, this means that communes have very similar and regular patterns of mobility through time, in the sense that if in a particular commune the Mobility index rises or falls steadily, then this index rises or falls steadily in the rest of the other MR communes. This, of course, does not mean that all communes have the same degree of mobility. What it implies is that the temporal evolution of mobility, aggregated at the communal level in a large city such as the MR, reflects very regular and similar patterns over time, which may be dictated by the routine activities of the city (e.g., well-defined travel routes to work during business days, well-established mechanisms in the supply chains).  
The effect of this global behavior can also be seen in the analysis of the commune mobility score (see Figure 2). The mobility score describes the relative mobility (percentiles in the score distribution) and shows high regularity and stability throughout the observation time for each commune. This regularity is sustained over time with a few variations and is not affected by confinement interventions. This fact, unlike the mobility index, makes the mobility score of little use, specifically to capture the effect of the confinement policies in the mobility of the MR communes, as was noted at the end of Section 3.1.