A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil

Human mobility · Mobile geolocation · Urban hierarchy· Spatial-temporal patterns · Temporal23 series · COVID-1924 1 Introduction25 The importance of human mobility during the COVID-19 outbreak has been clear since the beginning of the26 epidemic, in Wuhan, China in late December 2019, from where it spread throughout the highly connected27 network of tourism and business cities in the world, becoming a pandemic on March 11, 2020. It is not28 the first disease that used this pathway to move, since SARS and H1N1, for example, have also used it,29 but is certainly the most efficient one to do so in the last century. Since it is transmitted mainly through30 contaminated droplets of naso-oropharyngeal secretions from infected individuals, the rate of infections by31 the SARS-Cov-2 is related to human mobility in general, but more specifically to the close contacts between32 individuals of a population23.33 Mariana P. Melo Department of Basic and Environmental Sciences, Engineering School of Lorena, University of São Paulo, Lorena, Brazil. Cláudia P. Ferreira São Paulo State University (UNESP), Institute of Biosciences, Botucatu, São Paulo, Brazil Cláudia M. Peixoto· Sérgio M. Oliva· Diego Marcondes · Pedro S. Peixoto Department of Applied Mathematics, Institute of Mathematics and Statistics, University of São Paulo, São Paulo, Brazil . CC-BY-ND 4.0 International licenseIt 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 (which was not certified by peer review) The copyright holder for this preprint this version posted April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. 2 Cláudia P. Ferreira et al. As an emerging disease, very little was known about it, and, until the development of vaccines, there was34 no definitive scientific-based medical treatment or pharmaceutical prevention method for it. Therefore, its35 controlwasbasedmainlyonnon-pharmaceuticalmethodsseekingeithertoreducetheoddsofcontactwithan36 infected individual causing an infection, such as mask-use and hand washing, or to avoid the contact between37 an infected and susceptible individual, such as social distancing, lockdown, and detection and isolation of38 infected individuals. While the efficacy of mask-use and hand-washing, for example, may be quantified under39 controlled circumstances37, the efficacy of measures aiming to diminish the contacts between individuals40 through the decrease of human mobility may be hard to quantify. Besides, human mobility measures such41 as isolation indexes are often not accurate or hard to interpret31. In summary, the spread of COVID-19 is42 a multi-faceted complex process that is influenced by many uncontrollable variables, which may mask the43 effect of human mobility on it8, so it is difficult to establish a cause and effect relationship between an index44 of human mobility and the rate of infections20.45 Nevertheless, the pandemic spread has been frequently modeled by dynamical systems (deterministic or46 stochastic models)18 which usually have as control parameter some measure of amplification/attenuation of47 the disease infection rate due to different transmission scenarios of varying human contact. Human contact48 is indirectly measured through indices of human density, mobility, isolation, and social distancing. While in49 theory this is well accepted and provides insights on possible outcomes of the pandemic, it is usually very50 difficult to quantify the effects of non-pharmaceutical interventions on infection rates3,7,9, so most studies51 use ad hoctuning parameters40,38.52 Focusing on Brazil, it is the largest and most populated country of South America with around 210 million53 inhabitants. Although it is the 9th world economy, according to the International Monetary Fund27, it is54 a country marked by great inequalities and underdevelopment. Brazil is divided into five disparate regions55 (see Figure 1). The South and Southeast regions concentrate more than half the population, have the most56 developed infrastructure, are home to the wealthiest states and financial centers, offer better-paying jobs,57 and have better socio-economic indexes. The Midwest region, the least populated of them, is home to the58 country capital city Brasília, has a lower population density, consisting most of the agricultural land, and59 has socio-economic indexes lower than the southern regions, with the exception of the district of the capital60 city, which has better indexes. The North and Northeast regions are the poorest, with lower socio-economic61 indexes and underdeveloped infrastructure. Although both regions suffer from the lack of infrastructure, the62 situation is worse in the North, whose territory is covered by the Amazon rain forest, which makes logistics63 difficult in the region.64 The first case of COVID-19 in Latin America was confirmed on February 25 in a traveller returning to65 São Paulo city from the Lombardy region in Italy, the epicenter of the first wave of the disease in Europe,66 and the first death by the disease was reported on March 12, also in São Paulo. After that, with the epidemic67 evolving in Brazil, on March 20 the Ministry of Health recognized that community transmission was occurring68 across the country, as a strategy to ensure a collective effort and logistic and financial support for states69 and its population. This was followed by the implementation of nationwide non-pharmaceutical measures,70 including physical distancing, isolation, quarantine, compulsory notification, and mask-use mainly by elderly71 and exposed/infected people10.72 Due to a lack of national coordination, the pandemic was mainly fought by the 27 states and 5,56873 municipalities who took diverse, heterogeneous and mainly non-coordinated decisions by government officials74 at the federal, state and municipal levels. This led to both success and failure stories and to distinct efficacy75 of non-pharmaceutical measures in slowing the rate of transmission across the country, which outlined the76 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil 3 importance of taking into account the socio-economical background of a region when implementing such77 measures. Such a diverse response to the pandemic is this paper reason of being, since in a such heterogeneous78 scenario a much needed assessment of the efficacy of the measures to stop the disease spread is not a79 straightforwardtask,soacarefulquantitativeandqualitativeanalysisofthediseaseevolutionandofmeasures80 such as social isolation is needed to evaluate this efficacy.81 Fig. 1 Map of Brazilian regions and states abbreviations. This paper aims to asses the effectiveness of human mobility control measures on reducing the COVID-82 19 spread in Brazil, taking into account many aspects of the locations and their population, such as urban83 hierarchy, demography, and socio-economic profile. Our assessment focuses on the dataset containing daily84 cases of Severe Acute Respiratory Illness, and a daily isolation index, of the most important cities in Brazil85 in a period ranging from March 15 to October 30, 2020. We carefully dissect this dataset, coupling its86 quantitative analysis with qualitative information about measures enforced to slow the disease spread and87 characteristics of the population and locations around the country. With these analyses, we hope to give a88 snapshot of how the pandemic evolved in Brazil, and study the interplay between social isolation and COVID-89 19 spread in the country. Here we discuss and quantify in detail the conditions under which social distancing,90 measured through population local mobility, impact infection rates depending on different demography and91 socio-economic profiles. As a result, besides providing on its own insightful knowledge of the behavior of the92 pandemic in different conditions, our results allow models to be more precisely adjusted to take into account93 local characteristics and provide more reliable epidemic scenarios.94 In Section 2 we present the material and methods of the quantitative analysis, while in Section 3 we95 present its results, and in Section 4 we discuss our findings.96 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint 4 Cláudia P. Ferreira et al. 2 Material and Methods97 2.1 Data98 2.1.1 Human mobility99 The social isolation index is a relative measure of the amount of people that do not leave their houses during100 the day. It can be calculated based on mobile users’ mobility data from many private companies that work101 with geolocation services2,19,34,25. The government of São Paulo state, in cooperation with the 4 main mobile102 network services in Brazil (Oi, Tim, Vivo, Claro), publicly provide an official social isolation index for more103 than 100 cities of the state. The mobile network companies use radio based geolocation methods to infer104 the position of users, which limits its applicability, being adequate only for large cities with many stations.105 Google 19 and Apple2 only provide mobility data for a small subset of Brazilian cities.106 Due to the low coverage of brazilian cities of Google, Apple and Network companies, in this study,107 we adopt a dataset provided by the company InLoco∗ 25. This company provides anonymous geolocation108 technologies for several mobile applications. The Software Development kit provided by InLoco uses multiple109 mobile sensors, including Wi-Fi, GPS, bluetooth and other, to infer the mobile location with the accuracy of110 meters. The company does not collect any user personal information and users need toopt infor geolocation111 services in the application. Several safety measures are used to ensure data safety and the company complies112 with Brazilian law of data protection, which ensures ethical and legal assurances of data collection and113 usage 26.114 For the social isolation index, the home location of an user is estimated based on the recent location115 registered during night periods. Once the home location is known for each user in the database, InLoco116 calculates the number of users that left their homes during the day. The house location and the breach117 in isolation is calculated considering an Hexagonal hierarchical geospatial indexing system (H3 -https:118 //h3geo.org/) with resolution level 8 (hexagons have edges with approximately 460m of length). The H3119 data is further aggregated to city level. For this work, only aggregated city level with the isolation index120 pre-computed from the company was available, therefore avoiding any anonymity issues in what concerns121 this work.122 The main advantage of using the InLoco dataset is its wide coverage. In mid 2020 its database consisted123 of more than one fourth of the mobiles in the country†. While this data can have sample biases, with124 respect to the nature of the mobile application use and smartphone diffusion in the country, its is, to our125 knowledge, the vastest dataset of this kind for Brazil. Also, it has been widely used in the pandemic to126 monitor public efforts to reduce mobility and also in several academic studies5,6,14,32,33. All data used in this127 work is provided as supplementary material.128 In the analysis, for each municipality, the daily observed social isolation index was subtracted from the129 average value observed in the respective city from February 1 to February 15 (before carnival holiday and130 the start of the pandemic in Brazil). Therefore, in what follows, we will refer to the isolation index as being131 this difference from the reference period, interpreted as theincrement/reduction in social isolation.132 2.1.2 Reported cases133 The number of reported cases of Severe Acute Respiratory Illness (SARI), over time, was collected from the134 national database SIVEP-Gripe11. It comprises all severe hospitalized cases related to respiratory viruses135 ∗Recently the company changed name to Incognia †Due to a recent company shift in business area, the base suffered a reduction in size in 2021 and the company stopped providing the Social Isolation Index. . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil 5 whose notification is compulsory in Brazil. It has been a good thermometer to catch the disease spatio-136 temporal dynamics in the country, since it has struggled with an insufficient capacity of molecular diagnosis137 and fast tests21. The information available does not distinguish between imported and autochthonous cases.138 Although the first COVID-19 case occurred on February 25, the dataset used here ranges from March 15 until139 October 30, 2020, since before that changes were not yet implemented on the surveillance system of SIVEP-140 Gripe to identify COVID-19 cases among cases of other diseases such as Influenza, Respiratory Syncytial141 virus, Adenovirus, and Parainfluenza4. This period comprises the first wave of the disease in Brazil during142 which it is supposed the transmission of a unique variant of the virus in Brazilian territory.143 A nowcasting procedure was performed, using the R package NobBS30, to correct delay in notifications144 which in Brazil can take up to forty days. Since the nowcasted daily number of cases still presented weekly145 variations, it was smoothed by taking a 7-day moving average. To compare the disease spread among the146 cities, the daily number of cases was divided by 100,000 inhabitants.147 The effective reproduction numberRt was calculated using the nowcasted smoothed data of incidence.148 For this, we considered the epidemiological model SEIR (susceptible-exposed-infected-recovered), and the149 approach proposed by Wallinga and Lipsitch36. The parameters considered to calculateRt are the latent150 period (η−1) of 3.0 days, the infectious period (τ−1) of 6.4 days, and the life expectancy in Brazil (µ−1) of151 75 years. The rates of leaving the exposed and infectious classes are denoted bys1 =η +µ and s2 =τ +µ,152 respectively. Therefore, the generation interval distributiong(t) is given by1 153 g(t) = 2∑ i=1 s1s2esit 2∏ j=1,j̸=1 (sj −si) with t ≥ 0. After normalizingg(t) we can evaluateRt as154 Rt = b(t)∫∞ 0 b(t −a)g(a)da, and the daily transmission index is calculated asRt ×τ.155 2.1.3 Urban hierarchy, human development index, and transportation infrastructure156 One variable that can directly affect the spread of the epidemic over the country is the hierarchy of urban157 centers. In Brazil, the classification is done by Instituto Brasileiro de Geografia e Estatística (IBGE)24, and158 is based on territory management, offering of trade and services, financial services, offering of university159 education, media and communication markets, culture and sports, transportation services, agricultural ac-160 tivities, and international links. The urban hierarchy of Brazil has five levels: (i) Metropolises, (ii) Regional161 Capitals, (iii) Sub-Regional Centers, (iv) Zone Centers, and (v) Local Centers. The unit of this classification162 is the population arrangement consisting of the clustering of two or more municipalities and constitutes a163

framework of urbanization in the country. On each level, the main city that comprises the urban164 arrangement gives it its name.165 The Metropolises level comprise the main urban centers of Brazil divided into three sub-levels: Greater166 National Metropolis, National Metropolis and Metropolis. The only Greater National Metropolis is São167 Paulo (SP), listed as an alpha global city by the Globalization and World Cities Research Network, with168 21.5 million of inhabitants. The National Metropolises are the Federal District of Brasília (DF), with 3.9169 million inhabitants, and Rio de Janeiro (RJ), which has a population of 12.7 million. These three cities170 are also the main destination of travel within and from outside of Brazil. Finally, the Metropolis sub-level171 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint 6 Cláudia P. Ferreira et al. is composed by: Belo Horizonte (MG), Curitiba (PR), Florianópolis (SC), Fortaleza (CE), Goiânia (GO),172 Manaus (AM), Belém (PA), Porto Alegre (RS), Recife (PE), Salvador (BA), Vitória (ES) and Campinas173 (SP). All of them but Campinas are capital cities of their respective states. The average population of174 Metropolises is 3 millions, with Belo Horizonte being the most populous with 5.2 million inhabitants and175 Florianópolis and Vitória the less populous with 1 and 1.8 million, respectively.176 The second level, the Regional Capitals, are composed of 97 urban centers with regional influence, which177 aredividedinthreegroups:A,BandC.TheRegionalCapitalsAiscomposedof8capitalcitiesofstatesinthe178 Northeast and Midwest region, and the city of Ribeirão Preto (SP). These cities have a similar population179 size, varying between 0.8 and 1.4 million inhabitants, and share a direct relationship with Metropolises.180 There are 24 Regional Capitals B, ten of them in the South region, which have an average population of181 530 thousand inhabitants, the most populous being São José dos Campos (SP) with 1.6 million inhabitants.182 These cities are reference centers within their states, with the exception of state capitals Palmas (TO) and183 Porto Velho (RO) which also exerts influence on other states. The Regional Capitals C are formed by 64184 cities, 30 of them in the Southeast region, with average population size of 360 thousand inhabitants.185 The Sub-regional Centers level is composed of 352 cities with less complex management activities than186 Regional Capitals. The forth level, Zone Centers, is composed of 398 cities with less management activities187 and, finally, the fifth level, the Local Centers, is composed of 4.037 cities, that is, 82.4% of urban centers of188 Brazil with an average of 12.5 thousand inhabitants and whose influence is restricted to its own territorial189 limits.190 Socio-economic variables are also usually associated with disease spreading, and the Human Development191 Index (HDI) is known to be an important factor. The HDI combines measurements of life expectancy,192 education, and per-capita income. It ranges from 0,418 to 0,862 among the cities, while the states average193 ranges from 0,631 to 0,824. The index is generally greater on states in the center-south regions and lowest194 in the northern regions. Indeed, the higher average index can be found at São Paulo (SP), Santa Catarina195 (SC), and Distrito Federal (DF) and the lower at Pará (PA), Alagoas (AL), Maranhão (MA), and Piauí (PI).196 Lastly, transportation infrastructure vary in the country. Although the primary source of transportation197 is the road transportation, it is highly concentrated in the center-south regions, specially in the state of São198 Paulo. The exception to this rule is the Amazon region where road transportation loses its importance to199 waterways thanks to the dense natural river network. The lack of adequate roads in the North region and200 the logistical issues with connecting roads with waterway transportation are some of the bottlenecks of the201 region’s development. From a human mobility point of view, while the majority of trips within states are by202 road, the main mean of transportation between states are airplanes, that count with a network of around203 100 airports around the country. International airports are located at São Paulo (SP), Rio de Janeiro (RJ),204 Brasíla (DF), Belo Horizonte (MG), Campinas (SP), Salvador (BA), Fortaleza (CE), Recife (PE), Porto205 Alegre (RS), Florianópolis (SC), Manaus (AM), Belém (PA), Natal (RN), and Campo Grande (MS).206 3 Results207 3.1 Human mobility versus reported cases208 In this section, we study the relationship between the daily social isolation index and the daily incidence of209 the disease in the main cities that comprise the metropolises, which are São Paulo, Brasília, Rio de Janeiro,210 Belo Horizonte, Curitiba, Florianópolis, Fortaleza, Goiânia, Manaus, Belém, Porto Alegre, Recife, Salvador,211 Vitória, and Campinas. Similar to what was done for the daily incidence, the daily social isolation index212 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil 7 was smoothed by taking a 7-day moving average. Figure 2 shows the daily ratio between the social isolation213 index, and the daily incidence, and their respective daily average among the cities considered. Spatial-214 temporal variations of both measures highlight regional and temporal differences resulting from geographic,215 demographic, cultural and political characteristics of each main city of Brazil, whose behaviour affects other216 citiesintheirregionofinfluence.Ingeneral,thesocialisolationindexwasnegativelyrelatedwiththeincidence217 of the disease, but not linearly proportional. Besides, taking all cities together, the monthly average of the218 social isolation index decreased with time: from March to October they were (average value and its standard219 deviation), respectively,0.21 ± 0.02, 0.22 ± 0.02, 0.18 ± 0.03, 0.13 ± 0.01, 0.13 ± 0.02, 0.11 ± 0.01, 0.09 ± 0.01,220 and 0.08 ± 0.01.221 In order to mitigate the effects of the disease on the healthcare system, lockdown strategies were imple-222 mented on some cities in the North and Northeast regions, causing the sharp increase on the social isolation223 index measured in Belém, Fortaleza and Recife (see Figure 2 around May 10). In Belém, differently from224 the other two cities, the lockdown can be clearly seen in the data since its social isolation index was below225 average in the period leading up to the lockdown and then increased way over the average. For these cities,226 the epidemic peak was from 2.5 to 4.2 times the observed average incidence on their respective days.227 Among the cities of the Northeast region, there is Salvador, which seems to have kept a more efficient228 control of the disease transmission, since it endured a higher isolation rate, and had a smaller peak, compared229 to other cities of this region. On the other hand, there is Fortaleza, which has the lowest HDI among the230 three Northeast cities considered, and is one of the main entrance of travelers from outside the country231 visiting the North and Northeast regions, factors which can explain its low performance on controlling the232 spread of the disease relatively to the other two cities. Likewise, in the North region, despite the fact that233 the social isolation index was higher at Belém compared to Manaus, both cities had a similar epidemic234 temporal evolution pattern. Among the cities, these two cities have the lowest HDI and are highly connected235 by waterways. They belong to the Amazon region where the spread of COVID-19 took the course of the236 waterways and was enhanced by the long duration of the trips in boats, where mitigation strategies, such as237 socially distancing and hand washing, are compromised22.238 In the Southeast region, although an increase on the social isolation index was observed in Belo Horizonte239 at the end of the study period, it had a similar transmission pattern as Campinas, while Vitória, which is240 among the cities with the highest HDI and lacks an international airport, had the best performance on disease241 controltransmissionwhencomparedtotheotherSoutheastcities,whatcanbeduetotheseimportantfactors.242 Among the South cities, despite Curitiba not having an international airport, its has worse performance on243 the social isolation index when compared to Porto Alegre and Florianópolis, which may be behind its larger244 number of reported cases. Still in the South, it is worth mentioning that not only Florianópolis has a high245 HDI, but also a major part of its territory is an island, which could have contributed to its high performance246 on controlling the disease spreading when compared to the other South cities.247 When comparing both cities of the Midwest region, one sees that Goiânia had a social isolation index248 pattern similar to Brasília, but its performance to contain the spread of the disease was worse. The fact that249 Brasília has a higher HDI and lower population density may explain the low disease incidence compared to250 the other cities. Another important factor is that the Midwest region annually records the lowest number of251 influenza and other respiratory viruses cases inside the national territory13, so these cities might be prone252 to have lower incidence of a respiratory disease. Lastly, Rio de Janeiro and São Paulo, both Southeast cities,253 are highly connected by roadways and airways, and share a similar pattern of social isolation index, with254 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint 8 Cláudia P. Ferreira et al. São Paulo, in general, having a better performance. Differently from the others cities, São Paulo has been255 having an outbreak of COVID-19 always above the average.256 3.2 Lockdown strategy257 Strict lockdown strategies were not common in Brazil in 2020, but were nonetheless implemented in four258 capital cities of states in the northern regions. In Figure 3 we present the daily incidence (in brown) and the259 Rt (in blue) for four cities which implemented a lockdown, namely, São Luís, Belém, Fortaleza and Recife.260 Among the four cities, the first confirmed case occurred in Recife on March 12, which was then followed by261 Fortaleza on March 15, Belém on March 18, and São Luís on March 20. The disease spread differently in262 each city, which also have distinct hospital and test capacities. The first city to declare lockdown was São263 Luís on May 5 when it achieved 10.75 new cases per day (average of the 7 days before lockdown). It was264 then followed by Belém on May 7 with 7.14 new cases per day, Fortaleza on May 8 with 11.35 new cases per265 day, and Recife on May 16 with 8.17 new cases per day. In São Luís, the lockdown took 13 days, and it was266 observed a reduction of 32.5% on the number of cases per day. In Belém it took 18 days with a reduction of267 19.8% on the number of cases per day. In Fortaleza it took 24 days with a reduction of 33.6% of the cases268 per day. Finally, in Recife it took 16 days with a reduction of 8% on the number of cases per day.269 In Figure 3, the orange vertical band represent the declaration of an emergency situation, characterized by270 the closing of schools, universities, bars, shopping malls, commerce, etc. In green we had the flexibilization271 of some measurements, and in red the lockdown period. Table 1 shows different measures on the data272 calculated before, during and after the lockdown period. This analysis was done considering a lag of seven273 days (≈ incubation period) between the social isolation index and the daily incidence.274 In all cases, the lockdown was effective on reducing the incidence (andRt values). This control method275 was clearly efficient in São Luís, which was presenting an increase on the rate of transmission before lockdown276 that changed to a decreasing pattern after it. Fortaleza, Belém and Recife were already diminishing the rate277 of transmission before lockdown occurred. Among them, Fortaleza was able to keep it longer with a high278 social isolation index. Although having a huge increase on social isolation index as a result of lockdown,279 Recife was not able to keep it for long. As a consequence, theRt value after lockdown was similar to the one280 measured before it. It is interesting to note that in Recife the social isolation index was already increasing281 before lockdown.282 For São Luís, the maximum incidence occurred six days before lockdown, and after lockdown disease283 incidence still decreased until fifteen days after it ended. For Belém, the maximum incidence occurred sixteen284 days before lockdown, and after lockdown the incidence still decreased until five days after it ended. For285 Fortaleza, the maximum incidence occurred five days before lockdown, and after lockdown the incidence still286 decreased until ten days after it ended. For Recife, the maximum incidence occurred eighteen days before287 lockdown, and after lockdown the incidence still decreased until fifteen days after it ended. The highest288 percentage on the reduction of the infection observed in São Luís can be related to its lower position on289 the urban hierarchy when compared to the other three, and to its spatial geography (it is an island). All290 these cities have public laboratories for the molecular diagnosis of SARS-CoV-2, but we can not compare the291 diagnostic capacity of each one because this data is not publicly available. The lack of diagnostic capacity292 can jeopardize control efforts by causing delay on decision making.293 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil 9 3.3 São Paulo mitigation strategies294 The history of SARS-Cov-2 spreading on the State of São Paulo is characterized by different time and spatial295 scales.Startingfromtheregionalcenters,thediseasedisplacedtomunicipalitieswithmajorconnections,after296 to municipalities with minor connections, and lastly to rural municipalities (spatial pattern well explained297 by the gravity model). Locally, the spread was by contiguity (diffusion model)16. As the disease spread,298 following the example of the metropolitan region of São Paulo, the inner state adopted strong mitigation299 measures closing schools, universities, and all its trade, keeping only essential services such as pharmacies,300 supermarkets, and hospitals open. This delayed the arrival of the virus to the inner state by at least one301 month, letting the cities prepare their healthcare systems, which are more fragile in this region.302 On May 27, São Paulo State started to move out from a restrictive quarantine with a flag system that303 classifies, based on several indicators, the disease transmission risk, and the probability of break-down of the304 healthcare system. Five colors were adopted: (i) red (phase 1) is considered a contamination phase and only305 essential services are permitted; (ii) orange (phase 2) is considered an attention phase, with the possibility of306 some services opening (limit of 20% of its capacity and maintaining all specific hygiene protocols); (iii) yellow307 (phase 3) is considered a controlled phase, with some flexibilization (limit of 40% of its capacity and main-308 taining all specific hygiene protocols); (iv) green (phase 4) is a partial opening phase, in which all services are309 allowed to open (limit of 60% of its capacity and maintaining all specific hygiene protocols); (v) blue (phase310 5) has only restrictions over events that generate large agglomeration of people. Restaurants, fitness centers,311 cultural activities, and beauty salons are allowed from phase 3. At phase 4, schools and universities can312 be opened with 35% of the classes occupied (Plano São Paulo, https://www.saopaulo.sp.gov.br/planosp/).313 These phases were attributed to each region of the State, defined according to a division of its healthcare314 system 12. These regions, called Regional Health Departments (DRS, in portuguese), are each one represented315 by a major centralized city: Araraquara, Araçatuba, Baixada Santista, Barretos, Bauru, Campinas, Franca,316 São Paulo Metropolitan Area, Marília, Piracicaba, Presidente Prudente, Registro, Ribeirão Preto, São João317 da Boa Vista, São José do Rio Preto, Sorocaba, and Taubaté .318 Figure 4 shows the temporal evolution of the incidence (in brown) and theRt (in blue) for selected319 cities in São Paulo State. The relation between the transmission index and the social isolation index is also320 displayed (with a lag of seven days between them). The other colors (vertical bands) are associated with321 each moment of the São Paulo’s Plan in each city. The peak of the incidence curve occurred on May 5 at São322 Paulo (with 6 new cases) on June 10 at Campinas (with 5.9 new cases), and on August 10 at Votuporanga323 (with 8.5 new cases). This pattern shows the spread of the disease from the metropolis of São Paulo to324 inner cities in a lower degree of urban hierarchy. Besides, less complex cities (less level of urban hierarchy325 compared to São Paulo) were not able to achieve a high social isolation index or keep it for a long time.326 The variance observed on the transmission rate can be related to the population density in each city which327 is respectively 7398.3, 1359.6, and 201.2 inhab/km2 at São Paulo, Campinas, and Votuporanga. Although328 the incidence was higher at Votuporanga, the average absolute number of cases was 3.4 (from 1 to 11), 36.3329 (from 9 to 95), and 422.8 (from 161 to 986) in Votuporanga, Campinas, and São Paulo, respectively.330 3.4 Relation between social isolation index and the speed of the disease dispersion331 In this section, we study the relationship between social isolation index and how fast the disease spread over332 different geographic locations around the country. The enrolled cities satisfy one of the following criteria: (i)333 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint 10 Cláudia P. Ferreira et al. is the capital of a state, (ii) is the first or second city of a state with a higher number of cases, (iii) belongs334 to São Paulo state and is among its cities with highest number of cases.335 For each municipality, the smoothed curve of daily cases in the upward phase, that is, from March 15336 until the day when the maximum number of cases occurred, was considered. Then, the upward phase was337 divided into seven stages in the following way. First, we calculated the total number of infected people in this338 period (upward phase), divided it in half and marked the day in which such a number of cases was reached339 as the start of stage 7, which ends when the peak of cases is reached. Therefore, stage 7 represents the340 period contemplating the second half of the cases until the peak. Analogously, new successive divisions were341 made, minding the day when a corresponding half of accumulated cases was reached. In total, six divisions342 were made, creating 7 stages. In this way, stage 1 refers to period between March 15 and the occurrence of343 1.5625% of the cases in the upward phase; stage 2 refers to period between 1.5625% and 3.125% of it; and344 stages 3 to 6 correspond to periods between 3.125%-6.25%, 6.25%-12.5%, 12.5%-25%, 25%-50%, respectively,345 of cases in the upward phase (see Figure 5).346 The length of these stages is an estimate of the speed of disease spreading. When efforts to stop or347 diminish the disease spread are implemented in one stage, one expects an increase in the length of later348 stages. Hence, finding a relationship between the efforts to control the disease spread, such as the social349 isolation index, and the length of these stages could be an efficient way of assessing the efficacy of the control350 measures.351 In Table 2 we present, for each municipality (a total of 31 analyzed), the median of the social isolation352 index and the length of the disease spreading stages. The incidence was associated to the social isolation353 index considering a lag of seven days. The social isolation index at dayt − 7 is the average between the ones354 observed att − 8, t − 7 and t − 6. In bold, are highlighted the values of the social isolation index above355 the third quartile (Q3) and the length of the stages (∆i with i = 1, 2,..., 7) which are above the respective356 median.357 Comparing the length of stages 5, 6, and 7 with their respective medians, we see that 24 municipalities358 (77.4%) maintain the same behavior, that is, they have the length of stages 5, 6, and 7 above the median or359 below the median in all three stages. Also, the correlation coefficients between the length of these stages are360 0.773 between stages 5 and 6, 0.691 between stages 5 and 7, and 0.849 between stages 6 and 7. Due to the361 similarity of these stages, plus the fact that they correspond to 87.5% of all cases in the upward phase, our362 analysis will be restricted to stage 7.363 Table 3 shows that a high social isolation index in stages 3 and 4, can slow the transmission of the disease364 in stage 7. From these 16 cities with length at stage 7 above the median, 12 (75%) of them had isolation365 above Q3 in stages 3 or 4. The four cities that did not had isolation above Q3 in these two stages were:366 Belo Horizonte, Guarulhos, Jundiaí and São Paulo. In the case of São Paulo, the length of the initial stages367 of disease spreading in this city was extremely short, indicating a fast initial dispersion of the disease. A368 social isolation index above Q3 was only observed in stages 5 and 6. This late high social isolation index may369 decrease the speed of disease, leading to the length of the final stages above of median. The city of Jundiaí370 had social isolation index above Q3 only in stages 1, 6 and 7, but presented a social isolation index above371 median in stages 2, 3 and 5. Therefore, except for stage 4, which was short (7 days), Jundiaí presented a372 social isolation index above the median in all the stages, which may have contributed to the reduction of the373 speed of disease transmission. On the other hand, we have the city of Guarulhos, that had a social isolation374 index above or equal the median in the stages 4, 5 and 6, and Belo Horizonte that had social isolation index375 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil 11 above of median in stage 4 and really close to the median in stage 5, which may have contributed to a376 duration superior than the median in the stage 7.377 Table 2 and 3 also present the cities at which the stage 7 length was below the median. From theses378 15 cities, 11 (73.3%) did not have social isolation index above Q3 in stages 3 or 4. The four cities which379 presented social isolation index above Q3 were: Aracaju, Boa Vista, João Pessoa and Salvador. Note that380 João Pessoa, Aracaju and Salvador had length of stage 7 equal to 19, 23 and 22 days, respectively, values381 which are close to the median 24. The city Boa Vista had social isolation index above Q3 in stage 3, however,382 it had social isolation index below first quartile (Q1) in stages 4, 5 and 6, which has contributed for the short383 duration of 18 days obtained in stage 7.384 The city that peaked faster was Manaus (35 days), followed by Belém (38 days), Recife and Rio de Janeiro385 (45 days), São Luiz (46 days), Duque de Caxias and Fortaleza (50 days). Among these cities, we can observe386 that Fortaleza kept the social isolation index above the median in all the stages. This bad performance to387 control the epidemics despite the high social isolation index can be related to the fact that this city is the388 main entrance of individuals coming from outside of the country to the North and Northwest of Brazil. Also389 the bad performance of Duque de Caxias can be explained by the fact that they are in the region of Rio de390 Janeiro influence.391 3.5 Daily number of cases and the social isolation index during the upward phase392 In this section, we evaluate, in detail, how the daily incidence is related to the social isolation index during393 the upward phase of the epidemic. Here, we divided the upward phase of the epidemiological curve into394 intervals. In each interval, we have either an increase or a decrease of the incidence. We defined an increase395 (or decrease) in the incidence if it is increasing (or decreasing) on the extreme points of the interval and we396 have at upmost two consecutive decreases (or increases) in the interior of the interval. The starting point, for397 each epidemic curve, corresponds to the calendar day at which8.113 accumulated cases per 100k inhabitants398 were achieved. This threshold was chosen based on the epidemic growth observed in São Paulo city since this399 value is equivalent to 1000 accumulated cases in this city. In this analysis, we consider all cities not under400 the direct influence of São Paulo†, with∆7 above or equal to the median, and social isolation index above401 Q3 in stages 3 or 4 (see Table 3), which were the cities with earlier high isolation, and a slower stage 7, which402 could be caused in part by this high isolation.403 As an example, we show in Figure 6 the daily incidence for the city of Porto Alegre where the days in404 which the incidence increases or decreases are highlighted in different colors. Besides the temporal evolution405 of the incidence, we plotted the daily social isolation index against the daily incidence. Several features can406 be observed in this figure. A higher social isolation index was observed at the beginning of the epidemic,407 which seems to have promoted an efficient control of the incidence. With time, the isolation index decreased,408 which may have caused the epidemic curve to oscillate as can be seen by the large number of colors in the409 figure until the 70th day. Bellow some threshold of the social isolation index (around 0.16) a sharp vertical410 increase of the incidence can be seen, that is the days in blue. The increase of the social isolation index after411 this explosion of cases does not seem to control of the epidemic. This is an indicative that maybe if the social412 isolation index was kept 0.16 unit above of the reference value measured in February, Porto Alegre could413 have avoided the explosion of cases observed after the 70th day.414 The dispersion plot between the daily incidence and social isolation, colored according to the increase or415 decrease in cases, is presented in Figures 7 and 8. Five of those cities are Metropolises, three are Regional416 †Hence we excluded Jundiaí and São Paulo from this analysis. . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint 12 Cláudia P. Ferreira et al. Capitals A and four are Regional Capitals B. A similar behavior was observed for the cities considered which417 have implemented some control measures in stages 3 or 4 (section 3.4) and are not under the influence of418 a Metropolis that did not do some mitigation control in these stages. For all these cities there seems to be419 a threshold, which may vary from city to city, where a decrease on the isolation index triggers an abrupt420 increase on the daily incidence. This phenomenon is characterized by theL-shape of the dispersion between421 the isolation index and daily incidence, where the horizontal part of theL refers to a period when higher422 isolation may have held the incidence low, and the vertical part of theL refers to a period when either the423 variation on the isolation does not affect the incidence or the decrease on the isolation below the threshold424 was followed by an explosion of cases.425 The cities Teresina and Porto Velho, where theL-shape is not observed, are in the region of influence of426 Fortaleza and Manaus, respectively, Metropolises that did not implemented mitigation strategies capable of427 increasing significantly social isolation, what could have caused the mitigation on these cities to not properly428 function. Indeed, Teresina has sustained an increase on the incidence although having a high social isolation429 index during the whole upward phase.430 Among the Metropolises, the number of monotone intervals varied between 2 and 5. Goiânia, the431 Metropolis in Midwest, had 2 intervals, Campinas, the Metropolis in the Southeast, had 3 intervals and432 the Metropolises in the South region had 3, 4 and 5 intervals (Curitiba, Porto Alegre and Florianópolis,433 respectively). The HDI values of these cities, in the order they were mentioned, are 0.799, 0.805, 0.823, 0.805434 and 0.847. Those localized in the South region presented a greater number of intervals, indicating that the435 adopted measures in these cities succeeded on breaking the increasing sequence. In the case of Florianópolis,436 since a major part of its territory in an island, other geographical feature could have contributed to control437 the disease spreading.438 For the Regional Capitals A, the numbers of intervals varied between 2 and 7. Teresina, localized in the439 Northeast region, had 2 intervals, while Cuiabá and Campo Grande, both in the Midwest region, had 5 and 7440 intervals, respectively. The HDI of these cities, in the order they were mentioned, are 0.751, 0.785 and 0.784.441 In this hierarchy, there are only capitals from Northeast and Midwest regions and the latter ones presented442 better results.443 Finally, for the 4 Regional Capitals B, the number of intervals varied between 2 and 5. Porto Velho,444 localized in the North region, had 2 intervals, while Palmas, from Midwest region and Londrina and Caxias445 do Sul, both from the South region, had 5 intervals. The HDI of these cities, in the order they were mentioned,446 are 0.736, 0.788, 0.778 and 0.782. The performance of Palmas on controlling the disease’s spreading could be447 explained by the influence of Goiânia over it. The Capital from the North region presented the worst result,448 that is, lower number of intervals, while Midwest and South regions presented the best results. This detailed449 analysis, considering the number of intervals, shows again the importance of the urban hierarchy, HDI and450 regional factors in the spreading of the disease.451 Analyzing the results of each hierarchy, it seems that the number of intervals increases as the HDI452 increases (correlation coefficients 0.90, 0.98 and 0.76 for Regional Capitals A, Regional Capitals B and453 Metropolises, respectively). Although there seems to exists a threshold of the social isolation index below454 which an explosion of cases occurs, its value vary among the cities. Therefore, besides human mobility, other455 factors are certainly influencing the velocity of the disease’s spread.456 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil 13 4 Discussion457 In this work, we explored some variables that can be responsible for the failure or success of the mitigation458 strategies to halt the spreading of the COVID-19 epidemic in the Brazilian territory. In particular, we459 focused on social isolation, since during this epidemic period it was one of the few strategies available,460 besides prophylactic measures such as the use of masks and personal hand-hygiene. Our analysis sought to461 associate two sets of temporal series, the social isolation index, and the incidence, exploring the relationship462 between these two data sets in different cities in Brazil looking for patterns and what can explain them.463 The first thing that we could notice is that there is no direct and simple relationship between the social464 isolation index and the incidence. In fact, the evolution of the disease is driven by multiple factors. Besides465 the social isolation index, the urban hierarchy, the human development index and human and trade mobility466 together can explain the behavior of the epidemic, as shown in Sections 3.1-3.3. Among those patterns, we467 could find a relation between the starting time of the implementation of the mitigation strategy and the468 time at which the peak was reached. Namely, the cities that successfully implemented the social isolation469 strategy in stages 3 or 4 reached the peak of incidence later. Moreover, among those cities, a threshold on470 the social isolation index could be found. This threshold holds at the begging of the epidemic and promotes471 an efficient control of the incidence. With time, the social isolation index decreased, and the number of cases472 sharply increased in such a way that high isolation measures did not work anymore.473 There are some limitations related to the data used here. The bias of the daily isolation index is not474 controlled. On top of that, the daily incidence data cannot capture the asymptomatic cases. Despite these475 limitations, we successfully pointed out some patterns related to these data. We also could hypothesize that476 at least two patterns of disease dispersion can be found in Brazil29,35,28: a hierarchical one at Southwest477 region (like São Paulo state)15 and a local diffusion type at Northeast (like Ceará state). We also hypothesize478 that the epidemic is synchronized in each Metropolis17,39. These are relevant topics to be pursued.479 Resource A vailability480 Lead Contact: PSP. Data and Code A vailability: The datasets and codes generated during this study481 are available at the GitHub repository Mdynhttps://github.com/pedrospeixoto/mdyn.482 Acknowledgments483 PSP was supported by grant # 16/18445-7, São Paulo Research Foundation (FAPESP) and by grant484 #301778/2017-5, National Council for Scientific and Technological Development (CNPq). The research485 of CPF is supported by grant #2019/22157-5, São Paulo Research Foundation (FAPESP) and by grant486 #302984/2020-8, National Council for Scientific and Technological Development (CNPq). DM was supported487 by the National Council for Scientific and Technological Development (CNPq) during the development of488 this paper.489 Author Contributions490 Data Curation, Formal Analysis and Investigation were mainly performed by CPF, MPM and CMP. All491 other aspects of the paper had active participation of all authors, including conceptualization, methodology,492 discussions, writing and review.493 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint 14 Cláudia P. Ferreira et al. Declaration of Interests494 The authors declare no competing financial or non-financial interests.495 References496 1. Akkouchi, M. (2008). On the convolution of exponential distributions. Journal of the Chungcheong497 Mathematical Society, 21(4):501–510. 5498 2. Apple (2021). COVID-19 Mobility Trends Reports.https://covid19.apple.com/mobility. Accessed:499 29th March 2021. 4500 3. Ball, F., Britton, T., House, T., Isham, V., Mollison, D., Pellis, L., and Tomba, G. S. (2015). Seven501 challenges for metapopulation models of epidemics, including households models.Epidemics, 10:63–67. 2502 4. Bastos, L. S., Niquini, R. P., Lana, R. M., Villela, D. A., Cruz, O. G., Coelho, F. C., Codeço, C. T.,503 and Gomes, M. F. (2020). Covid-19 and hospitalizations for sari in brazil: a comparison up to the 12th504 epidemiological week of 2020.Cadernos de Saúde Pública, 36:e00070120. 5505 5. Buss, L. F., Prete, C. A., Abrahim, C. M., Mendrone, A., Salomon, T., de Almeida-Neto, C., França,506 R. F., Belotti, M. C., Carvalho, M. P., Costa, A. G., et al. (2021). Three-quarters attack rate of sars-cov-2507 in the brazilian amazon during a largely unmitigated epidemic.Science, 371(6526):288–292. 4508 6. Candido, D. S., Claro, I. M., de Jesus, J. G., Souza, W. M., Moreira, F. R., Dellicour, S., Mellan, T. A.,509 Du Plessis, L., Pereira, R. H., Sales, F. C., et al. (2020). Evolution and epidemic spread of sars-cov-2 in510 brazil. Science, 369(6508):1255–1260. 4511 7. Chang, S., Pierson, E., Koh, P. W., Gerardin, J., Redbird, B., Grusky, D., and Leskovec, J. (2021).512 Mobility network models of covid-19 explain inequities and inform reopening.Nature, 589(7840):82–87. 2513 8. Cot, C., Cacciapaglia, G., and Sannino, F. (2021). Mining google and apple mobility data: temporal514 anatomy for covid-19 social distancing.Scientific reports, 11(1):1–8. 2515 9. Cota, W., Soriano-Paños, D., Arenas, A., Ferreira, S. C., and Gómez-Gardeñes, J. (2021). Infectious dis-516 ease dynamics in metapopulations with heterogeneous transmission and recurrent mobility.arXiv preprint517 arXiv:2102.10614. 2518 10. Croda, J., Oliveira, W. K. d., Frutuoso, R. L., Mandetta, L. H., Baia-da Silva, D. C., Brito-Sousa, J. D.,519 Monteiro, W. M., and Lacerda, M. V. G. (2020). Covid-19 in brazil: advantages of a socialized unified520 health system and preparation to contain cases.Revista da Sociedade Brasileira de Medicina Tropical, 53.521 2522 11. da Saúde, S.-M. (2020). Srag 2020 - banco de dados de síndrome respiratória aguda grave - incluindo523 dados da covid-19. https://opendatasus.saude.gov.br/dataset/activity/bd-srag-2020. Accessed:524 15th November 2020. 4525 12. de Almeida, G. B., Pronunciate, M., Grotto, R. M. T., Pugliesi, E. A., Guimarães, R. B., Vilches, T. N.,526 Coutinho, R. M., de Castro Catão, R., Ferreira, C. P., and Fortaleza, C. M. C. B. (2020). Two hundred527 days of covid-19 in são paulo state, brazil.Epidemiology & Infection, 148. 9528 13. de Mello Freitas, F. T. (2013). Sentinel surveillance of influenza and other respiratory viruses, brazil,529 2000–2010. The Brazilian Journal of Infectious Diseases, 17(1):62–68. 7530 14. Dias, F. L., Assumpção, M., Peixoto, P. S., Bianchi, M. B., Collaço, B., and Calhau, J. (2020). Using531 seismic noise levels to monitor social isolation: An example from rio de janeiro, brazil.Geophysical Research532 Letters, 47(16):e2020GL088748. 4533 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil 15 15. Fortaleza, C. M. C. B., Guimarães, R. B., Catão, R. d. C., Ferreira, C. P., Berg de Almeida, G.,534 Nogueira Vilches, T., and Pugliesi, E. (2021). The use of health geography modeling to understand early535 dispersion of covid-19 in são paulo, brazil.PloS one, 16(1):e0245051. 13536 16. Fortaleza, C. M. C. B., Guimarães, R. B., de Almeida, G. B., Pronunciate, M., and Ferreira, C. P. (2020).537 Taking the inner route: spatial and demographic factors affecting vulnerability to covid-19 among 604 cities538 from inner são paulo state, brazil.Epidemiology & Infection, 148. 9539 17. Geoghegan, J. L., Saavedra, A. F., Duchêne, S., Sullivan, S., Barr, I., and Holmes, E. C. (2018). Con-540 tinental synchronicity of human influenza virus epidemics despite climactic variation.PLoS pathogens,541 14(1):e1006780. 13542 18. Giordano, G., Blanchini, F., Bruno, R., Colaneri, P., Filippo, A. D., Matteo, A. D., and Colaneri, M.543 (2020). Modelling the covid-19 epidemic and implementation of population-wide interventions in italy.544 Nature Medical, 26:855–860. 2545 19. Google (2021). Google COVID-19 Community Mobility Reports.https://www.google.com/covid19/546 mobility/. Accessed: 29th March 2021. 4547 20. Grantz, K. H., Meredith, H. R., Cummings, D. A., Metcalf, C. J. E., Grenfell, B. T., Giles, J. R., Mehta,548 S., Solomon, S., Labrique, A., Kishore, N., et al. (2020). The use of mobile phone data to inform analysis549 of covid-19 pandemic epidemiology.Nature communications, 11(1):1–8. 2550 21. Grotto, R. M. T., Lima, R. S., de Almeida, G. B., Ferreira, C. P., Guimarães, R. B., Pronunciate, M.,551 Azevedo, E., de Castro Catão, R., and Fortaleza, C. M. C. B. (2020). Increasing molecular diagnostic552 capacity and covid-19 incidence in brazil.Epidemiology & Infection, 148. 5553 22. Guimarães, R. B., CATÃO, R. D. C., MARTINUCI, O. D. S., PUGLIESI, E. A., and Matsumoto, P.554 S. S. (2020). O raciocínio geográfico e as chaves de leitura da covid-19 no território brasileiro.Estudos555 Avançados, 34(99):119–140. 7556 23. Hâncean, M.-G., Slavinec, M., and Perc, M. (2021). The impact of human mobility networks on the557 global spread of covid-19.Journal of Complex Networks, 8(6). Accessed: 09th April 2021. 1558 24. IBGE, R. d. J. (2018). Regiões de influência das cidades.IBGE. RJ. 5559 25. Inloco (2021a). Mapa brasileiro da COVID-19. https://mapabrasileirodacovid.inloco.com.br/.560 Accessed: 29th March 2021. 4561 26. Inloco (2021b). PolÃtica de Privacidade: Inloco x COVID-19. https://www.incognia.com/pt/562 politicas/covid. Accessed: 29th March 2021. 4563 27. IPRI (2017). As 15 maiores economias do mundo. https://www.funag.gov.br/ipri/index.php/564 o-ipri/47-estatisticas/94-as-15-maiores-economias-do-mundo-em-pib-e-pib-ppp . Accessed:565 4th April 2021 - Instituto de Pesquisas de Relacoes Internacionais. 2566 28. Kuebart, A. and Stabler, M. (2020). Infectious diseases as socio-spatial processes: The covid-19 outbreak567 in germany.Tijdschrift voor economische en sociale geografie, 111(3):482–496. 13568 29. Kuo, C.-L. and Fukui, H. (2007). Geographical structures and the cholera epidemic in modern japan:569 Fukushima prefecture in 1882 and 1895.International Journal of Health Geographics, 6(1):1–10. 13570 30. McGough, S. F., Johansson, M. A., Lipsitch, M., and Menzies, N. A. (2020). Nowcasting by bayesian571 smoothing: A flexible, generalizable model for real-time epidemic tracking.PLoS computational biology,572 16(4):e1007735. 5573 31. Nussbaumer-Streit, B., Mayr, V., Dobrescu, A. I., Chapman, A., Persad, E., Klerings, I., Wagner, G.,574 Siebert, U., Christof, C., Zachariah, C., and Gartlehner, G. (2020). Quarantine alone or in combination575 with other public health measures to control covid–19: a rapid review.Cochrane Database of Systematic576 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint 16 Cláudia P. Ferreira et al. Reviews, Issue 4. Art. No.: CD013574. 2577 32. Peixoto, P. S., Marcondes, D., Peixoto, C., and Oliva, S. M. (2020). Modeling future spread of infections578 via mobile geolocation data and population dynamics. an application to covid-19 in brazil. PloS one,579 15(7):e0235732. 4580 33. Sabino, E. C., Buss, L. F., Carvalho, M. P. S., Prete Jr, C. A., Crispim, M. A. E., Fraiji, N. A., Pereira,581 R. H. M., Parag, K. V., Peixoto, P. d. S., Kraemer, M. U. G., Oikawa, M. K., Salomon, T., Cucunuba,582 Z. M., Castro, M. C., Souza Santos, A. A., Nascimento, V. H., Pereira, H. S., Ferguson, N. M., Pybus,583 O. G., Kucharski, A., Busch, M. P., Dye, C., and Faria, N. R. (2021). Resurgence of covid-19 in manaus,584 brazil, despite high seroprevalence.The Lancet, 397(10273):452–455. 4585 34. SafeGraph (2021). Social Distancing Metrics. https://docs.safegraph.com/docs/586 social-distancing-metrics. Accessed: 29th March 2021. 4587 35. Schærström, A. (2014). Disease diffusion.The Wiley Blackwell Encyclopedia of Health, Illness, Behavior,588 and Society, pages 411–416. 13589 36. Wallinga, J. and Lipsitch, M. (2007). How generation intervals shape the relationship between growth590 rates and reproductive numbers.Proceedings of the Royal Society B: Biological Sciences, 274(1609):599–591 604. 5592 37. World Health Organization, . J. . (2020). Advice on the use of masks in the context of covid-19:interim593 guidance. https://apps.who.int/iris/handle/10665/332293.CCBY-NC-SA3.0IGO. Accessed: 01th594 April 2021. 2595 38. Yechezkel, M., Weiss, A., Rejwan, I., Shahmoon, E., Ben-Gal, S., and Yamin, D. (2021). Human mobility596 and poverty as key drivers of covid-19 transmission and control.BMC public health, 21(1):1–13. 2597 39. Zheng, M., Zhao, M., Min, B., and Liu, Z. (2017). Synchronized and mixed outbreaks of coupled recurrent598 epidemics. Scientific reports, 7(1):1–11. 13599 40. Zhou, Y., Xu, R., Hu, D., Yue, Y., Li, Q., and Xia, J. (2020). Effects of human mobility restrictions on600 the spread of covid-19 in shenzhen, china: a modelling study using mobile phone data.The Lancet Digital601 Health, 2(8):e417–e424. 2602 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil 17 A T ables603 T able 1 Percentage variation of the social isolation index and the transmission index per period. From the first to the fourth, period means week. In the case of Fortaleza and Recife, the fifth period is also a week. For all of them, the second week corresponds to the lockdown. In all cases, the last period is counted until the first minimum of the incidence curve after the lockdown period is finished. A lag of seven days between the isolation index and the transmission index was considered. São Luis Belém Fortaleza Recife Period isol. index trans. index isol. index trans. index isol. index trans. index isol. index trans. index - -0.0031 0.0176 -0.0164 -0.1907 -0.0196 -0.1368 0.0484 -0.0758 1 0.1134 -0.3595 0.0318 -0.2165 0.1303 -0.2813 0.1529 -0.1278 2 -0.0533 -0.1035 0.0115 -0.1293 -0.0471 -0.2425 -0.1080 0.0300 3 -0.2704 -0.1086 -0.1722 -0.1130 -0.0927 -0.1462 -0.1995 -0.0410 4 -0.1716 -0.0513 -0.1800 -0.0945 -0.1632 0.0986 -0.1562 -0.0758 5 - - - - -0.1544 0.0574 -0.0545 -0.0058 6 T able 2 Median of social isolation index and length of the stages (∆i with i = 1, 2, 3, 4, 5, 6, 7) of the upward phase for each municipality. The stage 1 refers to period between March 15 and the occurrence of 1.5625 % of the cases in the upward phase and the stage 2 refers to period between 1.5625% and 3.125% of it. The stages 3 to 7 correspond to periods between 3.125%-6.25%, 6.25%-12.5%, 12.5%-25%, 25%-50% and 50%-100% of cases in the upward phase, respectively. Median of Social Isolation Index Length of the stage i City Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6 Stage 7 ∆1 ∆2 ∆3 ∆4 ∆5 ∆6 ∆7 Aracaju 0.0452 0.1075 0.2833 0.2241 0.2000 0.1814 0.1900 6 4 12 15 16 17 23 Belém 0.0605 0.1120 0.0986 0.2401 0.2432 0.2051 0.2376 5 3 6 5 5 7 7 Belo Horizonte 0.0703 0.0180 0.0811 0.2658 0.2308 0.1781 0.1332 2 3 4 11 24 35 30 Boa Vista 0.0293 0.0797 0.2375 0.1509 0.1020 0.1329 0.1870 3 10 10 13 16 14 18 Campinas 0.0526 0.0893 0.1328 0.2984 0.2404 0.2025 0.1702 4 4 7 14 25 26 31 Campo Grande 0.0304 0.0895 0.2579 0.1921 0.1258 0.1065 0.1107 5 4 10 26 48 32 43 Caxias do Sul 0.0142 0.0920 0.0948 0.3095 0.1959 0.1287 0.1175 3 4 5 14 24 31 35 Cuiabá 0.0710 0.2483 0.1993 0.1395 0.1258 0.1349 0.1424 11 9 24 23 19 28 49 Curitiba 0.0723 0.0246 0.0884 0.2907 0.2363 0.1700 0.1519 3 2 6 11 23 36 34 Duque de Caxias 0.0628 0.0246 0.0870 0.1421 0.2277 0.1903 0.2059 3 2 4 6 8 10 17 Florianópolis 0.0716 0.0251 0.1023 0.3920 0.2765 0.1809 0.1553 3 2 6 8 33 36 30 F ortaleza 0.0694 0.0680 0.1233 0.2717 0.3008 0.2670 0.2552 4 2 3 8 10 11 12 Goiânia 0.0696 0.2809 0.2234 0.1727 0.1323 0.1292 0.1302 9 10 20 23 26 26 45 Guarulhos 0.0372 0.0379 0.0987 0.2740 0.2339 0.2064 0.1655 4 3 6 10 17 25 46 João Pessoa 0.0545 0.0525 0.0974 0.3032 0.2401 0.2361 0.2141 4 2 6 12 15 12 19 Jundiaí 0.1212 0.0864 0.1563 0.1434 0.2605 0.2786 0.2893 4 2 3 7 19 24 28 Londrina 0.0249 0.0845 0.0878 0.2942 0.2309 0.1361 0.1180 5 3 6 9 23 32 43 Manaus 0.0798 0.0450 0.1149 0.1020 0.2191 0.2372 0.2479 3 2 3 4 6 7 10 Natal 0.0570 0.0728 0.1160 0.2601 0.2239 0.1960 0.1874 4 3 9 16 16 15 19 Palmas 0.0347 0.0466 0.2021 0.1622 0.1260 0.0951 0.0901 3 6 10 21 15 37 48 Porto Alegre 0.0793 0.0193 0.1251 0.3402 0.3043 0.2264 0.1926 3 2 4 9 24 41 37 Porto V elho 0.1069 0.2608 0.2196 0.2119 0.1962 0.1731 0.1656 13 3 8 9 13 17 24 Recife 0.0751 0.0333 0.1253 0.2593 0.3255 0.2820 0.2937 3 2 4 8 7 8 13 Rio Branco 0.0499 0.1045 0.0983 0.2461 0.2114 0.1979 0.1886 6 2 5 6 8 12 19 Rio de Janeiro 0.0664 0.0241 0.0748 0.1510 0.2900 0.2472 0.2476 2 2 4 6 8 9 14 Salvador 0.0678 0.1030 0.2802 0.2872 0.2677 0.2381 0.2385 4 5 9 13 13 16 22 São Luís 0.0840 0.0437 0.0941 0.2095 0.2525 0.2135 0.2384 3 3 5 7 6 9 13 São Paulo 0.0720 0.0399 0.0182 0.0967 0.2673 0.2709 0.2286 1 2 2 4 9 17 24 Sobral 0.0515 0.0985 0.1989 0.2720 0.2161 0.2031 0.1795 6 4 5 14 10 11 10 T eresina 0.0582 0.0632 0.1018 0.3089 0.2433 0.2110 0.2137 4 3 6 15 19 18 26 Vitória 0.0312 0.0595 0.1037 0.2625 0.3015 0.2572 0.2127 4 1 3 8 11 19 22 Median 0.0628 0.0680 0.1149 0.2593 0.2339 0.2025 0.1886 4 3 6 10 16 17 24 3rd Quartile 0.0718 0.0953 0.1991 0.2890 0.2639 0.2367 0.2331 5 4 8.5 14 23 29.5 34.5 . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint 18 Cláudia P. Ferreira et al. T able 3 Distribution of municipalities according to social isolation index and disease transmission speed. The stage 1 refers to period between March 15 and the occurrence of 1.5625 % of the cases in the upward phase and the stage 2 refers to period between 1.5625% and 3.125% of it. The stages 3 to 7 correspond to periods between 3.125%-6.25%, 6.25%-12.5%, 12.5%-25%, 25%-50% and 50%-100% of cases in the upward phase, respectively.∆7 is the lenght of stage 7 andQ3 is the third quartile. Social Isolation Index above Q3 Stages 3 or 4 Stages 1, 2, 5, 6 or 7 Aracaju Belém Boa Vista Fortaleza João Pessoa Manaus Municipalities with Salvador Recife ∆7 below or equal to median Rio Branco Rio de Janeiro São Luís Sobral Vitória Campinas Jundiaí Campo Grande São Paulo Caxias do Sul Cuiabá Curitiba Municipalities with Florianópolis ∆7 above or equal to median Goiânia Londrina Palmas Porto Alegre Porto Velho Teresina ∗The municipalities of Belo Horizonte, Duque de Caxias, Guarulhos and Natal did not have an isolation index above the third quartile at any stage . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil 19 B Figures604 0.6 0.8 1 1.2 1.4 1.6 03/21 05/10 06/29 08/18 10/07 (a) isolation/average group isolation date National Metropolis Brasília Rio de Janeiro São Paulo 0.6 0.8 1 1.2 1.4 1.6 03/21 05/10 06/29 08/18 10/07 (b) isolation/average group isolation date Northwest Salvador Fortaleza Recife 0.6 0.8 1 1.2 1.4 1.6 03/21 05/10 06/29 08/18 10/07 (c) isolation/average group isolation date North Manaus Belém 0 1 2 3 4 03/21 05/10 06/29 08/18 10/07 (d) incidence/average group incidence date National Metropolis Brasília Rio de Janeiro São Paulo 0 1 2 3 4 03/21 05/10 06/29 08/18 10/07 (e) incidence/average group incidence date Northwest Salvador Fortaleza Recife 0 1 2 3 4 03/21 05/10 06/29 08/18 10/07 (f) incidence/average group incidence date North Manaus Belém 0.6 0.8 1 1.2 1.4 1.6 0 50 100 150 200 (g) isolation/average group isolation date Southwest Belo Horizonte Campinas Vitoria 0.6 0.8 1 1.2 1.4 1.6 03/21 05/10 06/29 08/18 10/07 (h) isolation/average group isolation date South Porto Alegre Florianópolis Curitiba 0.6 0.8 1 1.2 1.4 1.6 03/21 05/10 06/29 08/18 10/07 (i) isolation/average group isolation date Midwest Goiânia 0 1 2 3 4 03/21 05/10 06/29 08/18 10/07 (j) incidence/average group incidence date Southwest Belo Horizonte Campinas Vitória 0 1 2 3 4 03/21 05/10 06/29 08/18 10/07 (k) incidence/average group incidence date South Porto Alegre Florianópolis Curitiba 0 1 2 3 4 03/21 05/10 06/29 08/18 10/07 (l) incidence/average group incidence date Midwest Goiânia 1 Fig. 2 In (a-c), (g-i) the daily ratio between the social isolation index and its respectively daily average. In (d-f) and (j-l) the daily incidence and its respectively daily average. The average was calculated considering the main cities that represent each Metropolis. The date corresponds to the day of the first symptoms. The dashed horizontal line shows when this ratio is equal to 1. . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint 20 Cláudia P. Ferreira et al. 0 2 4 6 8 10 12 14 16 03/21 05/10 06/29 08/18 10/07 0 1 2 3 (a) incidence/100k Rt date São Luis 0 2 4 6 8 10 12 14 16 03/21 05/10 06/29 08/18 10/07 0 1 2 3 (b) incidence/100k Rt date Belém 0 2 4 6 8 10 12 14 16 03/21 05/10 06/29 08/18 10/07 0 1 2 3 (c) incidence/100k Rt date Fortaleza 0 2 4 6 8 10 12 14 16 03/21 05/10 06/29 08/18 10/07 0 1 2 3 (d) incidence/100k Rt date Recife 1 Fig. 3 Temporal evolution of incidence andRt, respectively in brown and blue. In orange, red and green, we have the start of control measurements, the lockdown and some degree of flexibilization, respectively. In (a) we have São Luís, (b) Belém, (c) Fortaleza, and (b) Recife. The date corresponds to the day of the first symptoms. The dashed horizontal line is drawn for Rt = 1. . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil 21 0 2 4 6 03/17 05/28 08/08 10/10 0 1 2 3 (a) incidence/100k Rt data São Paulo 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 (b) transmission index isolation index São Paulo 0 2 4 6 03/17 05/28 08/08 10/10 0 1 2 3 (c) incidence/100k Rt data Campinas 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 (d) transmission index isolation index Campinas 0 2 4 6 8 10 03/17 05/28 08/08 10/10 0 1 2 3 (e) incidence/100k Rt data Votuporanga 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 (f) transmission index isolation index Votuporanga 1 Fig. 4 São Paulo (DRS I), Campinas (DRS XII), and V otuporanga (DRS XV). In (a), (c), (e) the temporal evolution of incidence andRt, respectively in brown and blue. In (b), (d), (f) the isolation index versus the transmission index (with a lag of seven days between them). The colors in all panels represent the levels of São Paulo plan. The date corresponds to the day of the first symptoms. The (daily social) isolation index was subtracted from the average value observed from February 1 to February 15, and the (daily) transmission index is calculated asRt ×τ where τ −1 is the infectious period. . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint 22 Cláudia P. Ferreira et al. Fig. 5 Temporal evolution of the number of cases for the municipality of Aracaju. The date corresponds to the day of the first symptoms, measured from (t=0) March, 15. The stage 1 refers to period between March 15 and the occurrence of 1.5625 % of the cases in the upward phase and the stage 2 refers to period between 1.5625% and 3.125% of it. The stages 3 to 7 correspond to periods between 3.125%-6.25%, 6.25%-12.5%, 12.5%-25%, 25%-50% and 50%-100% of cases in the upward phase, respectively. Fig. 6 (a) Temporal evolution of the daily incidence and (b) the dispersion between the daily incidence and the isolation index for the city of Porto Alegre. The colors refer to periods of days where the incidence increases or decreases for at least three in a row. The downward phase of the incidence curve is in black. . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint A snapshot of a pandemic: the interplay between social isolation and COVID-19 dynamics in Brazil 23 Fig. 7 Dispersion between the daily incidence and the isolation index for the cities of (a) Campinas-SP, (b) Campo Grande-MS, (c) Caxias do Sul-RS, (d) Cuiabá-MT, (e) Curitiba-PR and (f) Florianópolis-SC. The colors refer to periods of days where the incidence increases or decreases for at least three in a row. Only the upward phase is considered. . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint 24 Cláudia P. Ferreira et al. Fig. 8 Dispersion between the daily incidence and the isolation index for the cities of ((a) Goiânia-GO, (b) Londrina-PR, (c) Palmas-TO, (d) Porto Alegre-RS, (e) Porto Velho-RO and (f) Teresina-PI. The colors refer to periods of days where the incidence increases or decreases for at least three in a row. Only the upward phase is considered. . CC-BY-ND 4.0 International licenseIt 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 April 30, 2021. ; https://doi.org/10.1101/2021.04.29.21256267doi: medRxiv preprint