key: cord-0264809-jtpj439w authors: Rocha, T. M.; Mendes, J. F.; Moret, M. A. title: Impact and effectiveness of social distancing for COVID-19 mitigation -- A transnational and transregional study date: 2021-09-05 journal: nan DOI: 10.1101/2021.09.01.21262990 sha: 7f9d5288e668765fcd427e7ddad7da60fe2cfceb doc_id: 264809 cord_uid: jtpj439w We present a detailed analysis of the relationship between the infection rate by SARS-CoV-2 and a distancing index based on COVID-19 Community Mobility Report by Google, for all states in the United States and Brazil, its most populous counties and municipalities, respectively, and all the 22 European Economic Community countries and the United Kingdom, with Google data and at least one thousand deaths by COVID-19 in 2020. We discuss why the infection rate is a proper choice to perform this analysis when analyzing a wide span of time. A strong Spearman's rank order correlation between the social distancing index and the infection rate in each locality. As a side result, we show that mask mandates increase the values of Spearman's correlation in the United States, where a mandate was not universally adopted. We also obtain a numerical relationship between the infection rate and the social distancing metric introduced in the present work. The current COVID-19 pandemic is the main health crisis in the world in a century, with over 209 million cases and 4.3 million deaths (1) . Starting in China in the end of 2019 (2) , it spread to all countries in the world, with waves occurring at different moments of time in each locality. A number of interventions were implement all over the world, such as travel ban, social distancing and mandatory mask use (3, 4) , and its effects have been discussed in different works, which generally concluded that they were effective in reducing the growth of cases and deaths (5) (6) (7) (8) (9) (10) . Possibly the more effective being lock-downs, workplaces and business closing and school closing, i. e. the social distancing policies (11) , with travel restrictions expected to have modest effects in reducing transmission with a high circulation of the virus (12) . mobility data and growth rates at earlier stages, but a weaker correlation at later stages of the pandemic, for 25 counties in the United States. We present here a transnational and a transregional analysis of the effect of social distancing for 22 European countries, the United States and Brazil, and a similar transregional study for the 50 and 27 states of the United States and Brazil, and the most populous cities and municipalities in each, respectively. These different localities represent greatly different situations and histories of the pandemic. For instance, as mask use became mandatory at different moments for American states we were able also to obtain some quantitative evidence on its effect in enhancing the effects of social distancing policies. Our main goal is to obtain an explicit social distancing data and the value of the infection rate, with the proportion of susceptible individuals estimated from an epidemiological model calibrated from the tine series of deaths in each locality (21) . As a proxy for the "amount" of social distancing we define a metric quantifying the deviation from a base-line representing the pre-pandemic normality. This is far from a simple task and many possibilities exist, and different mobility data are available from different sources (22-25). We require that data is freely available, with coverage up to the city level. For the above cited sources only Google mobility trends satisfies these two criteria, providing data on the following six categories of locations: retail and recreation (D 1 ); grocery and pharmacy (D 2 ); parks (D 3 ); transit stations (D 4 ); workplaces (D 5 ) and residential (D 6 ), as percentages of variation of time spent in each type of place, with respect to a base line defined for the period of January,3 to February, 6 2020. An increase (positive value) of the variation of time spent at residence is considered as a positive contribution to the isolation index, while the other five categories contribute with a negative sign. The social distancing index is then defined as a weighted average of the data for each category, with the corresponding sign, with weights given by an (arbitrarily) estimated average proportion of the duration of a day spent in each type of location, 3 and given by where, for illustration purposes, we added the value of 100, such that the baseline is close to this value, with no effect of the value of the Spearman's correlation. The resulting mobility index M for each Brazilian and American state are shown in (Figs. S1A) and (S1B), respectively, with a similar behavior of M for the other localities (not shown). The infection rate can be estimated as (26): where C is the average number of contacts of one individual per day, and P c the average probability of contagion of a susceptible individual from a single contact with an infected individual. Social distancing acts by reducing the number of contacts C, while other non-pharmaceutical interventions reduce the value of P c . We consider the following localities: • All 50 United States states, from the first reported case up to December, 20 2021. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted September 5, 2021. • The 24 United States counties with a population of at least one million and at least 1000 deaths in 2020 (Nassau was not considered due to inconsistent data for the number of deaths), from the first reported case in each county up to December, 20 2021. For estimations of susceptible population in Eq. (2) we use the an epidemiological model described in (21) to determine the attack rate in each locality. Serological surveys also provide such estimates, but are not available usually for every locality and for the required time window. The estimation of R t is discussed in detail in the supplementary material and the model in (21) is calibrated using the time series of deaths in order to avoid the significant under-notification of cases (28) . The results for the Spearman's rank-order correlation (29) between the social distancing metric M and the infection rate β for each locality are show in (Fig. 1) . In order to assess the effect of mandatory mask use in each United States county and state we compute r s for two periods: for the whole period cited above and indicating the percentage of time with a mask mandate, and for the period with a mask mandate only, for those counties with a mask mandate for at least 50% of the days since the beginning of the pandemic. For the remaining counties we 5 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted September 5, 2021. ; https://doi.org/10.1101/2021.09.01.21262990 doi: medRxiv preprint consider the whole period and mark the corresponding histogram in black. We also computed the Spearman's correlation for each of the six mobility data reported by Google, with results shown in (Fig. 2 ) and (Fig. 3) . The average of β/γ, over the time period considered for each locality, versus the total number of deaths at the end of each period is shown in (Fig. 4 ). An approximately linear relation, except for a few cases in Brazil, is clearly visible. A proper choice of a variable to represent the current circulation of the virus is central to asses the effects of mitigation policies. The infection rate as expressed in Eq. (3) is affected by the reduction of social contacts, which at its turn impacts the value of the average number contacts C, and by other implemented protocols, such as mask wearing, that reduce the probability of contagion per contact P c . On the other hand, the effective reproduction number R t , or any other measure of growth rate of the pandemic, also depends on the current attack rate, and confuses variables in the analysis. This is an important point to consider as a more detailed analysis requires a large data set, and therefore a larger time series, and therefore a significant variation of the attack rate (and consequently of the related proportion of susceptible individuals). Computing Spearman's correlation, rather than Pearson correlation for instance, allowed to put forward 6 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. We saw from (Fig. 4) that even a small increase in β, and thus a small decrease in M , for a long period of time, results in a significant increase in mortality. Our analysis does not grasp the impact of great gatherings of individuals and the possible effect of the so-called superspreading events (20) , or the implications of contact tracing. Future research considering socioeconomic and demographic data would certainly provide valuable information on mitigation strategies targeted at specific groups, such as elders and individuals with comorbidities, as well as the impact of school closure separately from other factors (30). We hope that the present work will contribute to a better assessment of the effects of social distancing, and at least partially of mask mandate, on the still ongoing mitigation interventions against the COVID-19 pandemic. This work received financial support from the National Council of Technological and Sci- is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted September 5, 2021. ; https://doi.org/10.1101/2021.09.01.21262990 doi: medRxiv preprint . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted September 5, 2021. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted September 5, 2021. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted September 5, 2021. 14 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted September 5, 2021. ID IN IA KS ME MT NV OH OR TX UT VT WY AR CA CO CT DE IL KY LA MD MA MI MN MS MO NE NH NJ NM NY NC ND OK PA RI SC SD TN VA WA WV . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted September 5, 2021. ; https://doi.org/10.1101/2021.09.01.21262990 doi: medRxiv preprint COVID-19 Dashboard by the Center for Systems Science and Engineering Human mobility and COVID-19 transmission: a systematic review and future directions Attack rate and the price of SARS-CoV-2 herd immunity in Brazil