Mining Google and Apple mobility data: Temporal Anatomy for COVID-19 Social Distancing
MMining Google and Apple mobility data:Temporal Anatomy for COVID-19 Social Distancing
Corentin Cot, , Giacomo Cacciapaglia, , ∗ Francesco Sannino , Institut de Physique des deux Infinis de Lyon (IP2I),UMR5822, CNRS/IN2P3, F-69622, Villeurbanne, France University of Lyon, Universit´e Claude Bernard Lyon 1, F-69001, Lyon, France CP3-Origins & the Danish Institute for Advanced Study, Danish IAS,University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark Dipartimento di Fisica “E. Pancini”, Universit`a di Napoli Federico II & INFN sezione di Napoli,Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, 80126 Napoli, Italy ∗ To whom correspondence should be addressed; E-mail: [email protected]
We employ the Google and Apple mobility data to identify, quantify and clas-sify different degrees of social distancing and characterise their imprint on thefirst wave of the COVID-19 pandemic in Europe and in the United States. Weidentify the period of enacted social distancing via Google and Apple data, in-dependently from the political decisions. Interestingly we observe a generaldecrease in the infection rate occurring two to five weeks after the onset ofmobility reduction for the European countries and the American states.
COVID-19 has disrupted our way of living with long lasting impact on our social behaviourand the world economy. At the same time, differently from earlier pandemics, a very largeamount of data has been collected ( ) thanks, also, to our smartphone dominated society.1 a r X i v : . [ phy s i c s . s o c - ph ] S e p martphones run mobility applications, such as Google and/or Apple Maps, that help humansnavigate. The mobility information stemming from these apps has been harvested by Googleand Apple, which have subsequently made it publicly available on the following websites:Google and Apple.In this paper we mine these data to quantify and characterise the effects of social distanc-ing measures enacted by various European countries and American states. An early study ofmobility effects on the pandemic evolution in China can be found in Ref. ( ). The Google mo-bility data, in Google wordings, show movement trends by region, across different categoriesof places. As categories we will use “Residential” and “Workplace”, which best describe thechange in people’s behaviour after the implementation of social distancing measures with re-spect to a baseline day. The latter is defined, according to Google, as the median value from the5-week period from the 3rd of January to the 6th of February, 2020, predating the wide spreadof the virus in Europe. The data show how visitors to (or time spent in) categorised placeschanged with respect to the baseline day. For Apple, the available mobility data represent a rel-ative volume of direction requests per country/region, sub-region or city, compared to a baselinevolume defined on the 13th of January, 2020. We will be using, from Apple, information about“Driving” and “Walking”, assuming they represent the time spent by people away from home.For the United States (US), only “Driving” data are available.Another set of data relevant for this work is related to the virus spreading dynamics, whichwe take from the website https://ourworldindata.org/. We normalise the data of each country ascases per million inhabitants.The data relative to the total number of infected cases are effectively parameterised using theHigh Energy Physics inspired formalism introduced in ( ), dubbed epidemic RenormalisationGroup (eRG). The approach has been generalised to take into account the spreading dynamicsacross different regions of the world in ( ) and the evolution of the second wave pandemic2cross Europe in ( ). The advantage of the eRG formalism resides in the limited number ofcoefficients needed to classify the spreading dynamics for each country. More complicatedmodels have been used in the literature to study the effect of non-pharmaceutical interventions,including mobility, for Europe ( ) and the US ( ), with the latter mostly focusing on localcommunities.Without further ado, following (
5, 6 ), we introduce α ( t ) below α ( t ) = ln ( I ( t )) , (1)where I ( t ) is the total number of infected cases per million inhabitants in a given region and ln indicates its natural logarithm. The function α ( t ) turns out to be well described by the followinglogistic function: α ( t ) = ae γt b + e γt . (2)Here, a represents the logarithm of the final number of infected cases per million inhabitants, b denotes the temporal shift from the start of the pandemic and γ measures the flatness of thecurve of the number of new infected cases. Here, and in the following, we will measure thetime t in weeks, so that γ is measured in inverse weeks. It was argued in (
5, 6 ) that, aside fromthe trivial temporal shift provided by b and for the first wave of the pandemics, two numbersare sufficient to characterise the evolution of the number of infected cases per each region, i.e. a and γ . This fact helps studying the correlation between mobility data and the virus spreadingdynamics for each region. By going beyond the previous parameterisation, we will discovera finer temporal structure directly related to the effects of the imposed lockdown and socialdistancing measures in the different regions.In this work we focus on a selection of European countries and all of the US states. InEurope, we considered countries with more than 3 million inhabitants and for which the datawere available. Note that we will only consider the period during which the first wave of the3OVID-19 was raging in Europe and in the US.Using Google and Apple data, we provide a rationale to identify the timing of the socialdistancing measure actualisation in each region. European countries and US states adopted dif-ferent degrees of social distancing measures during the first wave of the COVID-19 pandemic.Moreover the severity of the measures changed during the spreading of the epidemic withineach region of the world. This is why we defined the beginning of the impact of social distanc-ing measures in terms of the reduction in the mobility of individuals, rather than on politicaldecisions.We mine Google’s Residential and Workplace mobility data since they show movementtrends across different places compared to a reference period before the implementation of anymeasure. The Residential and Workplace data are best suited to quantify when and to whatextent people reduced their mobility and increased social isolation. Similarly, for Apple, wechoose Driving and Walking data for Europe and Driving for the US states, expressing them interms of a percentage reduction. Note that the Apple data refer to variations in the number ofsearches done on the Maps app, more details to be found on the website Apple.We define an immobility indicator (cid:31) M , as described in the section Methods in the supplemen-tary material, in terms of an average mobility reduction in the chosen categories. The averageis taken over six weeks after the beginning of social distancing. This indicator allows to sortthe European countries and the American states based on the hardness of social distancing. Wealso define regions with the highest rate of mobility reduction ( low mobility , LM) and regionswith the least reduction ( high mobility , HM), for Europe and the US separately. The results areshown in Fig. 1, were we indicate the LM regions in cyan and the HM regions in red, with acolour gradient representing different shades of mobility being proportional to the value of theindicator. For Europe, the countries with the smallest mobility grossly correspond to those thatimposed a lockdown, while the highest mobility country is Sweden, where no measures were4 LMHMImmobility indicator classificationCorrelation of mobility data
Apple Europe - - - - - - - - - - - -
200 Walking % D r i v i ng % Google Europe - - - - - % R e s i den t i a l % Google US - - - - - % ( Google ) R e s i den t i a l % ( G oog l e ) Figure 1:
The COVID-19 Mobility Map for Europe and the US . The two maps representrespectively the European and US states with different shades of mobility from the highest (HM)in bright red to the lowest (LM) in cyan. At the bottom of the figure there are three tadpole-like plots showing correlations between the four mobility reduction categories: Residential andWorkplace from Google, Driving and Walking from Apple. The head of the tadpoles correspondto the average over 6 weeks after social distancing begins, while the tail indicates a 8 weekaverage. The colour code in the three plots reflects the maps one. The maps are drawn withWolfram Mathematica.imposed. Nevertheless, even for Sweden the mobility data show a significant variation that al-lows us to define the beginning of social distancing despite the political decisions. Similarly forthe US states, the lowest LM corresponds to states in the North-East, California and Hawaii,which imposed lockdown measures. We also noticed that the beginning of the measures, as5efined by the mobility data in the US, corresponds to the dates when the schools were closedin each state ( ).To validate our conclusions, at the bottom of Fig. 1 we show the correlations betweenGoogle and Apple mobility data for Europe (left and central plot) and the US (right plot).Each region is represented by a tadpole-like symbol, with the head corresponding to the 6-weekaverage and the tail to the 8-week average. We label each country and state by using the samecolour code as in the maps. The plots show a clear correlation between the percentage changein each category. We also checked that the same correlation persists when comparing Googleto Apple categories.We now analyse possible correlations between mobility data and the parameters of the logis-tic function α ( t ) such as the infection rate γ and the log of the total number of infected cases a .To our surprise we find that γ is uncorrelated to the degree of mobility reduction. This impliesthat mobility changes have little impact on the velocity of diffusion of the disease. Of course,mobility data only capture one aspect of the social distancing, thus they do not offer a completepicture of the situation in various regions. This surprising finding can be interpreted in variousways. On the one hand, the result may imply that the main factor behind a reduction of γ couldlie in the behaviour of individuals in social occasions (mask wearing, proximity, greeting habits,to mention a few); on the other hand, it is quite possible that the value of γ does not representthe effect of the social distancing measures, as it derives from a global fit over a wide timescale.In other words, the fit values include both the measure and the pre-measure periods.To push further the analysis, we now explore whether social distancing measures (as definedvia the Apple/Google mobility data) lead to distinct temporal patterns in the European countriesunder study and the American states. In the eRG approach, γ is the natural parameter to use forthis task. We assume that, after the measures are enacted, there are two distinct temporal regionsdescribing the time dependence of the number of infected cases. These two regions, B and C6n the illustrative plot in Fig. 2e, are naturally described by two different gammas. We confirmthat such an analysis is possible via a MonteCarlo analysis. We then move to the actual dataand discover that two distinct temporal regions with their own gammas do emerge for severalregions. In Fig. 2 we show the outcome of the fit to the data in terms of the time interval ∆ t between the beginning of social distancing and its effects measured when the infection rate γ changes. We discover that most countries display a similar ∆ t . By fitting the distributions inFig. 2c to a gaussian, we find that to the two sigma level we have ∆ t = 2 . ± . weeks forEurope and ∆ t = 3 . ± . weeks for the US. The high compatibility of the two ranges showsthe emergence of a universal time scale for social distancing to be effective.Another important result is the general and strong reduction of the infection rate measuredwithin and after ∆ t both for Europe and the US, as shown in the left panels of Fig. 2 andsummarised by the red histograms of Fig. 2d. Discussion
We analysed the mobility data released by Google and Apple to quantify the effects of socialdistancing on the COVID-19 spreading dynamics in Europe and in the US. We were able toclassify different shades of social distancing measures for the first wave of the pandemic. Afteridentifying the countries according to their level of immobility, we observed a strong decreasein the infection rate occurring two to five weeks after the onset of mobility reduction for thecountries studied here. Another important result is the discovery of a universal time scale afterwhich social distancing starts showing its impact.We have also provided an actual measure of the impact of social distancing for each region,showing that the effect amounts to a reduction by % − % in the infection rate for mostcountries in Europe and % − % in the US. This is, to the best of our knowledge, a firstglobal and direct measure of the impact of social distancing. Interestingly, even countries that7 chematic division of regions A, B and C a)b) c)d) e) A B C t ( weeks ) ℐ ( t ) t ! S o c i a l d i s t a n c i n g s t a r t s S o c i a l d i s t a n c i n g e ff ec t s US A L AKA Z A RC A C O C T D E F L G A H II D I L I N I AKSKY L A M E M D M A M I M N M S M O M T N E N V NHN J N M N Y NCND O H O K O R PA R I S C S D T N T X U T V T VA W A W V W I W Y Δ t ( w ee ks ) A L AKA Z A RC A C O C T D E F L G A H II D I L I N I AKSKY L A M E M D M A M I M N M S M O M T N E N V NHN J N M N Y NCND O H O K O R PA R I S C S D T N T X U T V T VA W A W V W I W Y - - Δ γ ( % ) Europe F R A I T A ESP G B R D E U DN K CH E S W E SVK P R T P O L I R L N L D R O U B G R HR V N O R A U T HUN S R B BE L Δ t ( w ee ks ) F R A I T A ESP G B R D E U DN K CH E S W E SVK P R T P O L I R L N L D R O U B G R HR V N O R A U T HUN S R B BE L - - Δ γ ( % ) Figure 2:
Temporal anatomy of COVID-19 social distancing effects . In panel a), we show ∆ t and the percentage variation ∆ γ in the infection rate for the European countries consideredin this study. In panel b), we show the same for all the US states. In panels c) and d) we displaythe same results in the form of histograms, for Europe and the US separately, highlighting that ∆ t clusters around similar values. In panel e), we illustrate the subdivision of the first waveepidemic curve in three temporal regions: A before social distancing as defined via mobilitydata occurs, B until an effect is observed in the epidemic curve as a change in γ , and C coveringthe later times. ∆ t equals to the duration of the period B.did not impose political measures, like Sweden, show a reduction of the infection rate similar tothe ones experiencing a lockdown, suggesting that a certain degree of social restrain occurredregardless of the political decisions. Our results are compatible with early analysis of localsocial distancing measures taken in China ( ), where mobility data inter-cities from Baidu was8sed within a compartmental model.Using smartphone based open-source mobility data, we showed that it is possible to providea temporal anatomy of social distancing. We discovered the emergence of a characteristic timescale related to when social distancing effects have a measurable impact. This timing can alsobe used to quantify the impact of social distancing by determining the variation in infectionrate per country. Finding similar reduction, however, does not imply that the countries have asimilar number of infected cases per million inhabitants. It simply means that there has been achange in social behaviour. The result of this study, based on the simple eRG approach, lays thebasis for an effective tool for the authorities to evaluate the timing and impact of the impositionof social distancing measures, in particular related to movement restrictions. References
1. G. A. Wellenius, et al. , Impacts of state-level policies on social distancing in the unitedstates using aggregated mobility data during the covid-19 pandemic (2020).2. M. N. Lurie, J. Silva, R. R. Yorlets, J. Tao, P. A. Chan,
The Journal of Infectious Diseases (2020). Jiaa491.3. A. S. Islind, M. ´Oskarsd´ottir, H. Steingr´ımsd´ottir, Changes in mobility patterns in europeduring the covid-19 pandemic: Novel insights using open source data (2020).4. S. Lai, et al. , Nature (2020).5. M. Della Morte, D. Orlando, F. Sannino,
Front. in Phys. , 144 (2020).6. G. Cacciapaglia, F. Sannino, in press on Nature Sci. Rep. (2020).7. G. Cacciapaglia, C. Cot, F. Sannino, in press on Nature Sci. Rep (2020).9. S. Flaxman, et al. , Nature (2020).9. A. Kabiri, A. Darzi, W. Zhou, Q. Sun, L. Zhang, How different age groups responded to thecovid-19 pandemic in terms of mobility behaviors: a case study of the united states (2020).10. F. Nielsen, G. Marti, S. Ray, S. Pyne, Clustering patterns connecting covid-19 dynamicsand human mobility using optimal transport (2020).11. I. E. Fellows, R. B. Slayton, A. J. Hakim, The covid-19 pandemic, community mobilityand the effectiveness of non-pharmaceutical interventions: The united states of america,february to may 2020 (2020).12. B. Hong, B. Bonczak, A. Gupta, L. Thorpe, C. E. Kontokosta, Exposure density and neigh-borhood disparities in covid-19 infection risk: Using large-scale geolocation data to under-stand burdens on vulnerable communities (2020).13. F. Vanni, D. Lambert, L. Palatella, Epidemic response to physical distancing policies andtheir impact on the outbreak risk (2020).
Acknowledgements
G.C. and C.C. acknowledge partial support from the Labex-LIO (Lyon Institute of Origins)under grant ANR-10-LABX-66 (Agence Nationale pour la Recherche), and FRAMA (FR3127,F´ed´eration de Recherche “Andr´e Marie Amp`ere”).
Author contribution
This work has been designed and performed conjointly and equally by the authors. G.C., C.C.and F.S. have equally contributed to the writing of the article.10 ompeting interests
The authors declare no competing interests.
Materials and Methods
Immobility indicator.
European countries and US states adopted different degrees of socialdistancing measures during the first wave of the COVID-19 pandemic. Moreover the severity ofthe measures changed during the spreading of the epidemic within each country or state. Ratherthan classifying the countries based on their political choices, we use the mobility data providedby Google and Apple as indicators of the effective hardness of the measures.To find a measure for the immobility of a given population during the social distancingperiod, we define an average percentage variation for each of the four categories: Residentialand Workplace for Google and Driving and Walking for Apple (only Driving is available forUS states). For both mobility datasets, the percentage variations are defined with respect to areference date or period predating the exponential growth of the infection cases. The data aretypically very jugged, as illustrated in Fig. 3, mainly due to strong variations over the weekend.Furthermore, the mobility data feature a sharp decrease followed by a slow return to the pre-COVID-19 average. Taking into account this behaviour, it is necessary to define an averageover several weeks, which would allow us to associate a single number to each category andregion.Firstly, one needs to properly define the beginning of the social distancing period for eachregion: we choose to identify it with the time when Google Workplace percentage first dropsby 20% (at this time, typically, all mobility indicators have shown a significant variation). Theending of the measure period is harder to identify, as the social distancing measures have alwaysbeen lifted progressively ( ): this appears in the mobility data, as the curves gradually return11 urope SD measures 6 weeks after8 weeks after - - - - W o r k p l a c e s % SD measures 6 weeks after8 weeks after R e s i den t i a l % SD measures 6 weeks after8 weeks after - - D r i v i ng % SD measures 6 weeks after8 weeks after - - ( days ) W a l k i ng % US SD measures 6 weeks after8 weeks after - - - - W o r k p l a c e s % SD measures 6 weeks after8 weeks after R e s i den t i a l % SD measures 6 weeks after8 weeks after - - ( days ) D r i v i ng % Figure 3:
Raw Google and Mobility data.
In these plots we show a sample of raw Googleand Apple mobility data used in this work, for Europe (left) and the US (right). The time scaleis shifted so that the beginning of the social distancing, defined by a drop in Google’sWorkplace and indicated by the first vertical grey line, coincides for all countries and states.The other two vertical lines mark the end of the 6 and 8 week averaging periods respectively.We show the respective HM region in orange and the LM one in blue: for Europe, Sweden(orange) and Spain (blue); for the US, Wyoming (orange) and New York (blue).12o zero, i.e. to the reference period levels, or even above. Thus, we decided to fix the sameaveraging period for all the regions we considered. To test the robustness of our conclusions,we determine the outcome for two choices: 6 and 8 weeks after the effective beginning ofthe measures. The tadpole-like plot at the bottom of Fig.1 in the main text demonstrate thatthe duration of the averaging period, while changing the value of the mobility reduction, doespreserve the overall trend. In the following, therefore, we will use the 6-week average as ourbenchmark.To be able to classify the countries based on their immobility, we further define an immo-bility indicator as (cid:31) M ( region ) = (cid:88) j = cat. | p j ( region ) | max [ | p j | ] , (3)where | p j ( region ) | is the absolute value of the percentage variation in each category (labelledby j ). For each category, we divide by the maximal value observed in the pool. Note thatfor European countries we have 4 categories, so that (cid:31) M < , while for the US states we have3 categories, so that (cid:31) M < . We use this indicator to rank the European countries and theAmerican states from the ones with high mobility (HM) – small (cid:31) M – to the one with low mobility (LM) – large (cid:31) M . The values of the immobility indicator we obtain for the European countriesunder study and US states are shown in Fig. 4. The colour code ranges from the highest mobilityregion in bright red to the lowest mobility one in cyan, with gradient proportional to the valueof the immobility indicator. Comparing the virus spreading parameters with mobility data.
The epidemic evolutionof the first wave of the CODIV-19 pandemic can be effectively characterised by two parameters:the infection rate γ and the logarithm of the final number of total infected cases a ( ), measuredper million inhabitants. We remark, however, that it is risky to compare the number of infectedfor different regions due to the different procedures used when identifying the positive cases,13 urope F R A I T A ESP G B R D E U DN K CH E S W E SVK P R T P O L I R L N L D R O U B G R HR V N O R A U T HUN S R B BE L I mm ob ili t y i nd i c a t o r US A L AK A Z A R C A C O C T D E F L G A H I I D I L I N I A KS KY L A M E M D M A M I M N M S M O M T N E N V NH N J N M N Y NC ND O H O K O R PA R I S C S D T N T X U T V T VA W A W V W I W Y I mm ob ili t y i nd i c a t o r Figure 4:
Immobility indicator for the European countries and the US states.
Values of theimmobility indicator (cid:31) M for Europe (top) and the US (bottom). The colour code corresponds tothe ranking of each European country and each US state, matching the one used in Fig.1 of themain text.and the different testing rates and strategies. Thus, we assign more physical meaning to theinfection rates γ , which give an accurate temporal characterisation of the epidemic diffusion ineach region.It is, therefore, natural to hypothesise that regions with higher mobility may have a fasterdiffusion rate of the infection, i.e. larger values of γ . To test this hypothesis, in Fig. 5, we showthe Workplace, Residential and Driving reductions versus the infection rates for the Europeancountries in this study and the US states. To each country or state is associated a racecar-likesymbol: the pilot seat (dot) corresponds to the 6-week average, while the tail to the 8-weekaverage. Furthermore, the side bars indicate the error from the fits of the epidemic data. Thecolour codes match the immobility indicator defined above. The data used to generate the plots14igure 5: Infection rate compared to the mobility data . Racecar plots showing the fittedinfection rates γ versus the Google/Apple mobility categories. The vertical segment indicatesthe difference between 6 week (dot) and 8 week averages; the horizontal bars indicate the fiterror on γ .in Fig. 5 are reported in Tables 1 and 3, where we only report the mobility averages over 6weeks.Surprisingly, the data do not reveal any particular correlation between the values of γ andthe mobility data. As explained in the main text, this result can be interpreted in various ways.One possibility, which we will test in the following section, is that the γ from the fit of the firstwave is not the most appropriate measure, as it averages over the infection diffusion before andafter the mobility reduction occurs. 15 B C t ( weeks ) ℐ ( t ) ( weeks ) α ( t ) Figure 6:
Temporal anatomy of the first wave epidemic data . Left panel: schema of the 3temporal regions defined in the text. A refers to the pre-measure time, B occurs between thestart of the social distancing and the change in γ , C covers the later times, after the measureeffects occur. The duration of B is defined as ∆ t . Right panel: generating function (solid) andsample of the simulated points for the two-gamma model. Testing the two-gamma hypothesis.
We subdivide the period of the virus diffusion in 3 parts,as illustrated in the left panel of Fig. 6. Region A extends up to the time when the social distanc-ing starts, t = 0 , as defined from the mobility data; at this point Region B begins extending fora duration ∆ t ; finally Region C starts at t = ∆ t . As the beginning of Region B is determinedby the Google/Apple mobility data, we can probe the existence of a change in γ by fitting thedata in Region B+C with the following function: α γ ( t ) = a exp ( γ B t ) b + exp ( γ B t ) for t < ∆ ta exp ( γ C t ) b exp (( γ C − γ B )∆ t )+ exp ( γ C t ) for t > ∆ t (4)that depends on 5 parameters: a , b , γ B , γ C and ∆ t . We then extract the values of the 5 parame-ters by fitting to the data.We first test the effectiveness of our method by generating a mock set of data based on thefunction in Eq. (4), where we fix γ B = 0 . , γ C = 0 . and ∆ t = 20 days. An example of thegenerated data, overlaid to the generating function, is shown in the right panel of Fig. 6: thepoints are randomly generated within a one standard deviation region, i.e. [ N i −√ N i , N i + √ N i ] ,16 it parameters: first wave and 6-week average mobility variations in EuropeCountry ISO a γ b Work. Res. Driv. Walk.France FRA . . . × −
65 28 − − Italy ITA . . −
62 29 − − Spain ESP . . . × −
66 28 − − United Kingdom GBR . . −
59 23 − − Germany DEU . . . × −
39 14 − − Denmark DNK . . −
45 15 − − Switzerland CHE . . . × −
45 20 − − Sweden SWE . . . −
28 10 − . − Slovakia SVK . . −
45 17 − − Portugal PRT . . . × −
59 30 − − Poland POL . . . × −
41 17 − − Ireland IRL . . . × −
60 25 − − Netherlands NLD . . −
43 16 − − Romania ROU . . −
46 17 − − Bulgaria BGR . . −
42 16 − − Croatia HRV . . . × −
52 19 − − Norway NOR . . . × −
46 16 − − Austria AUT . . . × −
53 20 − − Hungary HUN . . . × −
42 17 − − Serbia SRB . . . × −
59 20 − − Belgium BEL . . −
57 24 − − Table 1:
First wave fits and average mobility reductions in Europe . Values of the fit for a , b and γ for the first wave in the 21 European countries considered in this study, together with the95% CL error. Six week average mobility reduction for Google and Apple categories.where N i is the number of cases per day as predicted by the generating function. We generated100 independent sets of mock data and fitted them to Eq. (4). We found that we can determinethe value of ∆ t within a range of two weeks. Furthermore, we define the percentage variationof the infection rate as ∆ γ = γ C − γ B γ C . (5)Having acquired confidence in the method, we now apply it to the real data. The results ofthe fits are reported in Tables 2 and 4. 17 it parameters: two-gamma function parameters in EuropeCountry ISO a γ B γ C b ∆ tFrance FRA . . . . × . Italy ITA . . . . Spain ESP . . . . × . United Kingdom GBR . . . . Germany DEU . . . . × . Denmark DNK . . . . Switzerland CHE . . . . × . Sweden SWE . . . . Slovakia SVK . . . × . . Portugal PRT . . . . × . Poland POL . . . . × . Ireland IRL . . . . Netherlands NLD . . . . × . Romania ROU . . . . × . Bulgaria BGR . . . . × . Croatia HRV . . . . × . Norway NOR . . . . Austria AUT . . . . × . Hungary HUN . . . × . Serbia SRB . . . . × . Belgium BEL . . . . . Table 2:
First wave fits for the two-gamma model for Europe . Outcome of the two-gammafits for the 5 parameters a , γ B , γ C , b and ∆ t . The errors refer to a 95% CL.18 it parameters: first wave and 6-week average mobility variations in the USState a γ b Work. Res. Driv.Alabama AL . . −
35 14 − Alaska AK . . . × −
36 14 − Arizona AZ . . . −
40 15 − Arkansas AR . . −
32 11 − California CA . . . −
46 20 − Colorado CO . . −
47 18 − Connecticut CT . . −
45 19 − Delaware DE . . −
43 17 − Florida FL . . −
42 17 − Georgia GA . . . −
41 16 − Hawaii HI . . . × −
45 20 − Idaho ID . . . × −
38 12 − Illinois IL . . −
45 19 − Indiana IN . . −
41 16 − Iowa IA . . −
34 14 − Kansas KS . . −
37 14 − Kentucky KY . . −
39 14 − Louisiana LA . . × −
39 15 − Maine ME . . . −
39 15 − Maryland MD . . . −
47 20 − Massachusetts MA . . −
51 22 − Michigan MI . . . −
51 20 − Minnesota MN . . −
43 19 − Mississippi MS . . −
34 13 − Missouri MO . . −
38 14 − Montana MT . . . × −
36 13 − Nebraska NE . . −
33 14 − Nevada NV . . −
50 18 − New Hampshire NH . . . −
42 18 − New Jersey NJ . . −
52 23 − New Mexico NM . . −
39 15 − New York NY . . −
53 22 − North Carolina NC . . . −
38 14 − North Dakota ND . . −
32 16 − Ohio OH . . . −
42 16 − Oklahoma OK . . −
36 13 − Oregon OR . . . × −
42 15 − Pennsylvania PA . . −
46 19 − Rhode Island RI . . . × −
43 18 − South Carolina SC . . −
36 13 − South Dakota SD . . . × −
31 14 − Tennessee TN . . −
38 14 − Texas TX . . −
41 17 − Utah UT . . . −
41 16 − Vermont VT . . . × −
47 18 − Virginia VA . . . −
42 17 − Washington WA . . −
48 18 − West Virginia WV . . −
37 13 − Wisconsin WI . . . −
39 17 − Wyoming WY . . −
33 13 − Table 3:
First wave fits and average mobility reductions in the US . Same as Table 1.19 it parameters: two-gamma function parameters in the USState a γ B γ C b ∆ tAlaska AK . . . . × . Arizona AZ . . . . × . Arkansas AR . . . . × . California CA . . . . × . Colorado CO . . . . × . Connecticut CT . . . . Delaware DE . . . . × . Florida FL . . . . × . Georgia GA . . . . Hawaii HI . . . . × . Idaho ID . . . . × . Illinois IL . . . . × . Indiana IN . . . . × . Iowa IA . . . . Kansas KS . . . × . . Kentucky KY . . . . Louisiana LA . . . . × . Maine ME . . . . × . Maryland MD . . . . × . Massachusetts MA . . . . Michigan MI . . . . Minnesota MN . . . . Mississippi MS . . . . × . Missouri MO . . . . × . Montana MT . . . . × . Nebraska NE . . . . × Nevada NV . . . . × . New Hampshire NH . . . . New Jersey NJ . . . . × . New Mexico NM . . . . × . New York NY . . . North Carolina NC . . . . North Dakota ND . . . . × . Ohio OH . . . . Oklahoma OK . . . . × . Oregon OR . . . . × . Pennsylvania PA . . . . × . Rhode Island RI . . . . × . South Carolina SC . . . . × . South Dakota SD . . . . × . Tennessee TN . . . . . Texas TX . . . . Utah UT . . . . Vermont VT . . . . × . Virginia VA . . . . × . Washington WA . . . . . West Virginia WV . . . . Wisconsin WI . . . . × . Wyoming WY . . . . . Table 4: