Radius of Gyration as predictor of COVID-19 deaths trend with three-weeks offset

Total and perimetral lockdowns were the strongest nonpharmaceutical interventions to fight against Covid-19, as well as the with the strongest socioeconomic collateral effects. Lacking a metric to predict the effect of lockdowns in the spreading of COVID-19 with, authorities and decision-makers opted for preventive measures that showed either too strong or not strong enough after a period of two to three weeks, once data about hospitalizations and deaths was available. We present here the radius of gyration as a candidate predictor of the trend in deaths by COVID-19 with an offset of three weeks. Indeed, the radius of gyration aggregates the most relevant microscopic aspects of human mobility into a macroscopic value, very sensitive to temporary trends and local effects, such as lockdowns and mobility restrictions. We use mobile phone data of more than 13 million users in Spain during a period of one year (from January 6th 2020 to January 10th 2021) to compute the users' daily radius of gyration and compare the median value of the population with the evolution of COVID-19 deaths: we find that for all weeks where the radius of gyration is above a critical value (70% of its pre-pandemic score) the number of weekly deaths increases three weeks after. The reverse also stands: for all weeks where the radius of gyration is below the critical value, the number of weekly deaths decreased after three weeks. This observation leads to two conclusions: i) the radius of gyration can be used as a predictor of COVID-19-related deaths; and ii) partial mobility restrictions are as effective as a total lockdown as far the radius of gyration is below this critical value.