Radius of Gyration as predictor of COVID-19 deaths trend with three-weeks offset
Authors: Hernando Alberto , Mateo David , Bayer Jordi , Barrios Ignacio 
Published: February 2021

AbstractTotal 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, 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.BackgroundAuthorities around the World have used lockdowns and partial mobility restrictions as major nonpharmaceutical interventions to control the expansion of COVID-19. While effective, the efficiency of these measures on the number of COVID-19 cases and deaths is difficult to quantify, severely limiting the feedback that can be used to tune the intensity of these measures. In addition, collateral socioeconomic effects challenge the overall effectiveness of lockdowns in the long term, and the degree by which they are followed can be difficult to estimate. It is desirable to find both a metric to accurately monitor the mobility restrictions and a predictor of their effectiveness.MethodsWe correlate the median of the daily radius of gyration of more than 13M users in Spain during all of 2020 with the evolution of COVID-19 deaths for the same period. Mobility data is obtained from mobile phone metadata from one of the major operators in the country.ResultsThe radius of gyration is a predictor of the trend in the number of COVID-19 deaths with 3 weeks offset. When the radius is above/below a critical threshold (70% of the pre-pandemic score), the number of deaths increases/decreases three weeks later.ConclusionsThe radius of gyration can be used to monitor in real time the effectiveness of the mobility restrictions. The existence of a critical threshold suggest that partial lockdowns can be as efficient as total lockdowns, while reducing their socioeconomic impact. The mechanism behind the critical value is still unknow, and more research is needed.