Impact of urban structure on COVID-19 spread
Javier Aguilar, Aleix Bassolas, Gourab Ghoshal, Surendra Hazarie, Alec Kirkley, Mattia Mazzoli, Sandro Meloni, Sayat Mimar, Vincenzo Nicosia, Jose J. Ramasco, Adam Sadilek
IImpact of urban structure on COVID-19 spread
Javier Aguilar, Aleix Bassolas, Gourab Ghoshal,
3, 4, ∗ Surendra Hazarie, Alec Kirkley, MattiaMazzoli, Sandro Meloni, Sayat Mimar, Vincenzo Nicosia, Jos´e J. Ramasco, † and Adam Sadilek ‡ Instituto de F´ısica Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), 07122 Palma de Mallorca, Spain. School of Mathematical Sciences, Queen Mary University of London,Mile End Road, E1 4NS, London, United Kingdom. Department of Physics & Astronomy, University of Rochester, Rochester, NY, 14627, USA. Department of Computer Science, University of Rochester, Rochester, NY, 14627, USA. Department of Physics, University of Michigan, Ann Arbor, MI, 48109, USA. Google, 1600 Amphitheatre Parkway, Mountain View, CA, 94043, USA. (Dated: July 31, 2020)The ongoing COVID-19 pandemic has created a global crisis of massive scale. Prior researchindicates that human mobility is one of the key factors involved in viral spreading [1–10].Indeed, in a connected planet, rapid world-wide spread is enabled by long-distance air-, land-and sea-transportation among countries and continents, and subsequently fostered by commutingtrips within densely populated cities [4, 6, 11–15]. While early travel restrictions contribute todelayed disease spread, their utility is much reduced if the disease has a long incubation period or ifthere is asymptomatic transmission [16–27]. Given the lack of vaccines, public health officials havemainly relied on non-pharmaceutical interventions, including social distancing measures, curfews,and stay-at-home orders [13, 22–26, 28–32]. Here we study the impact of city organization on itssusceptibility to disease spread, and amenability to interventions. Cities can be classified accordingto their mobility in a spectrum between compact-hierarchical and decentralized-sprawled [33–35].Our results show that even though hierarchical cities are more susceptible to the rapid spread ofepidemics, their organization makes mobility restrictions quite effective. Conversely, sprawled citiesare characterized by a much slower initial spread, but are less responsive to mobility restrictions.These findings hold globally across cities in diverse geographical locations and a broad range ofsizes. Our empirical measurements are confirmed by a simulation of COVID-19 spread in urbanareas through a compartmental model. These results suggest that investing resources on earlymonitoring and prompt ad-hoc interventions in more vulnerable cities may prove most helpful incontaining and reducing the impact of present and future pandemics.
The SARS-CoV-2 virus, believed to have originatedin the Hubei province of China around the end of2019 [36, 37], has since spread to 213 countries andterritories ( https://covid19.who.int/ ). Given thenovelty of the virus, the immunological susceptibility ofthe population, and the lack of a proven therapeuticor vaccine, the response toolbox of public healthauthorities has been limited to non-pharmaceuticalinterventions, such as recommending hand-washing andmore stringent hygienic measures, or imposing socialdistancing measures, travel restrictions, and populationconfinement via stay-at-home orders [13, 22–26, 28–32].Different countries, and often even different regionswithin each country, have adopted varying degrees ofmobility restriction measures in an attempt to containor at least slow down the spread. However, theeffect of these measures on the temporal evolution ofthe epidemics varies significantly across geographicalregions. The main reason behind such variabilityis likely to be that mobility itself is a multi-facetedphenomenon showing diverse characteristics at different ∗ Electronic address: [email protected] † Electronic address: jramasco@ifisc.uib-csic.es ‡ Electronic address: [email protected] spatiotemporal scales. Indeed, long-range mobility ismainly driven by air transportation, but restrictionsto international flights have shown limited utility inmitigating the propagation of infectious diseases unlessthey are applied very early and in a comprehensivemanner [19, 21, 24]. At a more granular level—withincountries, between provinces or states—transportationmodes include train and road traffic, in additionto air travel, while at an even finer scale —withincities— vehicular traffic, pedestrian, bike, and publictransportation modes are predominant [10, 38]. Inparticular, the unique mixture of different transportationmodes at an urban level and spatial organization ofactivities and residential areas creates specific mobilityfingerprints.We start with an overview of how lockdowns affectmobility and epidemic spreading at a global scale. Fig. 1 a explores the connection between mobility reduction andthe maximum incidence I max (the maximum number ofnew daily cases per-capita). The color-code used inthe map reflects the division of the two-variable spacedisplayed in the inset. Darker colors correspond to largerincidence peaks, and are therefore indicative of moresevere impacts. Although the pandemic is still evolvingas of this writing, some interesting trends are apparent.In some countries like Japan, South Korea, Sweden orparts of the US, the mobility reductions are in the a r X i v : . [ phy s i c s . s o c - ph ] J u l FIG. 1:
Impact of mobility restrictions on disease propagation at multiple scales a
Choropleth map of thehighest mobility reduction versus the maximum incidence ( I max ). The colors represent the division of thedistribution of I max and the maximum travel reduction across countries (see inset). The data corresponds to theperiod January-June 2020. b-g Scatter plot of R eff versus the corresponding mobility reduction one week before interms of total flow for b countries (the baseline mobility is taken 5 weeks before the onset of 100 cases), c Italianprovinces (baseline mobility: 2nd week of February), d Spanish provinces (baseline mobility: 2nd week of February), e South Korean provinces (baseline mobility: 2nd week of February), f Indian states (baseline mobility: 2nd week ofMarch), and g US cities (baseline mobility: 3rd week of February). Due to the early lockdown in India, we also showdata for 2 weeks before 100 cases. The dashed white line represent LOESS non-parametric fits, and the pale bluearea corresponds to the 95% CI. Details on the mobility dataset are in Methods, Supplementary Table 1 for theepidemiological data sources and Supplementary Table 2 for the list of countries considered.range 30-50% (detailed results by country are reported inSupplementary Fig. 1). However, the policies regardingtesting and other protection measures are quite diverseand so is the epidemic impact. On the flip-side, countrieslike India, Italy and Spain, enforced mobility reductionsby 80% in terms of total trip flows after the onset ofthe epidemics. The enforcement of lockdown policiesproduced both quantitative and qualitative differences insmall- and medium-scale mobility patterns. At countryscale, the trips suffering the most pronounced relativereduction are those in the medium-long distance range(see Supplementary Figs. 2-4). This means that the different areas and cities of the countries are significantlyless connected. In parallel, the weekly incidence of thedisease is quite heterogeneous, and its association withthe decrease of mobility is complex (see SupplementaryFig. 5).The temporal evolution of the disease as a functionof mobility reductions is shown in Fig. 1 b-g . The keyvariable here is the effective reproduction number R eff ,computed as in [39, 40], capturing the transmissibilityof the disease in the early stages of the local outbreakin each country. Each square of Fig. 1 b represents acountry and the colors correspond to different weeksfrom the outbreak onset. Mobility restrictions cause adecrease of R eff , and in about 2-3 weeks the effectivereproduction number approaches 1 (the threshold ofsustained spread) and the incidence reaches its peak. Asthe figure indicates, a decrease of internal country-levelmobility between 25% −
50% is often associated withsignificantly reduced propagation. A similar behavioris observed at a finer resolution in Fig. 1 c-f , where weshow Italian, Spanish and South Korean provinces, aswell as Indian states (see Supplementary Tables 3-6 forthe list of provinces and states). There is still a noticeablereduction in R eff when mobility restrictions are enforced,but its functional dependence on mobility changes. Forinstance, in Italy we observe the presence of a phasedlockdown, with a relatively smooth decrease in mobilityand R eff . In this specific case, a nearly total lockdowncorresponding to 80% reduction in flow was required tonoticeably slow propagation down. For Indian statesand Spanish provinces instead, we see an abrupt shiftwith a sudden transition from baseline mobility to 80%reduction, as an effect of a comprehensive and suddenlockdown. The case of South Korea is unique, mainlydue to the government’s choice of concentrating resourceson contact-tracing and large-scale testing, rather thanon mobility restrictions. The connection between flowreduction and R eff is therefore quite weak, as expected.Moving to even finer resolution, in Fig. 1 g we plot the50 largest metropolitan areas in the United States (SeeSupplementary Section 1 for a description of the OECDurban areas and Supplementary Table 7 for the list ofUS cities). The plot shows the same qualitative trendsseen in Italy and Spain, although the comparatively lowermobility reductions implemented in the US caused thespread of the disease to continue for longer in many cities( R eff > a-c , we show the spatial mobility layout for threecities arranged in increasing levels of centralization intheir mobility structure: Atlanta (Φ = 0 . . . a ). Instead, flows are sharply increased betweenthe new sprawled hotspots (Supplementary Figure 6 b ).Indeed, in the case of Chicago, we see the emergenceof suburban areas as hotspots, indicating that mobilityis localized within smaller areas, and there is limitedflow between locations. For the case of Atlanta, whichis sprawled to begin with, a few mobility hotspotsdisappear, and others emerge, but there is little-to-nochange in the spatial distribution. This can be seen inSupplementary Fig. 7, where we plot in decreasing orderthe fractional change in distance between hotspots dueto the mobility restrictions finding that centralized citiestend to get more spread out, whereas in sprawled cities,mobility hotspots remain spatially separated, suggestingthat mitigation measures have limited impact on theoverall mobility structure.In addition to the mobility-flows, we also haveincidence curves for each administrative unit associatedwith the city (e.g., counties, supplementary tables 9-30detail the list of counties considered per OCDE urbanarea). This allows us to run a granular analysis ofthe impact of lockdowns by investigating the extentto which specific areas of the city drive the epidemicspreading to other parts. To do so, we calculate theaverage Transfer Entropy, h TE i , between the incidencecurves for each subsets of the city (see Methods), andFIG. 2: Types of cities and COVID-19 spreading.
Maps with the changes in mobility hotspots before andafter the lockdown in three cities with different mobility hierarchy (higher Φ indicates more centralized cities): a-c
Atlanta, Chicago and New York City, respectively, in the week of February 2 for prelockdown mobility and the weekApril 5 for the postlockdown. d-e
The average Transfer Entropy h S T i , capturing the influence of an administrativedivision (county) to drive infection-spread as a function of time. Vertical red lines mark the date of the officiallockdown. After lockdown, the ability of a single region to drive infection spread dissipates, and the transmissionevolves independently in each area. g-i The temporal evolution of the effective reproduction number before andafter lockdown versus the mobility change one week before. Each symbol represents a county of the city. Whilesprawled cities like Atlanta have regions responding independently, in centralized New York City, we see a clearsynchronized and monotonically decreasing reduction in R eff as a function of mobility reduction.in Fig. 2 d-f plot the results as a matrix whose rowscorrespond to the administrative sub-unit, and columnscorrespond to weeks, starting from the onset of 100cases, to the first week of June. The elements inthe matrix are color-coded by the value of h TE i . Forall three cities, a few regions drive the spreading ofthe infection before lockdown, although the strengthof the driving is stronger on average in NYC andChicago compared to Atlanta (results for four othercities are reported in Supplementary Fig. 8). Oncelockdown is initiated (marked as vertical red lines), the driving becomes diffused, indicating the predominanceof localized spreading in sub-regions with little influenceon one another. The localization in spreading appears inparallel to the equivalent phenomenon in mobility, with arelative increase in self-flows and a decrease of inter-areaflows in the administrative units (Supplementary Fig.9). While the influence of each administrative unit oninfection-spreading dissipates in a similar fashion, thereis a key difference in how they are synchronized in termsof their response to mobility-mitigation. In Fig. 2 g-i , weplot R eff as a function of mobility reduction in each citywith points corresponding to sub-units and colored bytime-period. While in Atlanta we see that each regionmore or less responds independently in terms of reducingtransmission, for the case of Chicago we begin to see apattern emerging, that becomes clear when looking atNYC where the various regions are clustered temporallyand reduce transmission in a monotonically decreasingfashion with mobility-reduction.These patterns generalize beyond the three cities.In Fig. 3 a we plot R eff in the early stages of thepandemic (three weeks after onset of 100 cases) as afunction of the baseline Φ for the top 22 metropolitanareas in the United States by number of countieswith populations greater than two million inhabitants(full list of cities and their corresponding Φ listed inSupplementary Table 8). There is a clear connectionbetween transmissibility and mobility hierarchy, withhierarchical cities having an increased spread of thedisease at the onset. Indeed NYC being the mosthierarchical city in the United States, had a 50% highervalue of R eff than sprawled ones such as Cincinnati,Charlotte and Atlanta. This increased transmissibilityis also reflected in the extent of the spread of the diseaseas measured by plotting I max against Φ in Fig. 3 b .Cities can be separated into those that have alreadyexperienced a peak in the incidence curve (Northeasternand Midwestern cities, colored in yellow), and thosewhich are still at the early phases of the pandemic(Southern and Western cities, in red). Restricting tocities where the pandemic is already well-established,we see a clear trend whereby hierarchical cities havea much wider outbreak as compared to sprawled ones.Stronger mitigation strategies manifest in those placeswhere the outbreak is wide-spread [41], and a relationbetween mobility reduction and Φ emerges as can beseen in Fig. 3 c where we find that NYC, San Franciscoand Boston reduce mobility by around 60%, whereas onthe other end of the spectrum, Cincinnati, Minneapolis,Atlanta or Charlotte decrease mobility by around 40%.The connection between mobility reduction and reducedtransmission is also far more pronounced: plotting thePearson correlation between the reduction in R eff and thecorresponding change in total flow, the week before, asa function of Φ, indicates that hierarchical cities seemsignificantly more responsive to mitigation measures(Fig. 3 d ). In order to check the robustness of ourresults with respect to the uncertainties in the epidemicdata, we further confirm them using other data source inSupplementary Fig. 11.The empirical results (Figs. 2 and 3) suggest thatcentralized cities experience faster and more widespreadoutbreaks as compared to sprawled ones. However,mobility restrictions and lockdowns in those cities arecomparatively more effective. To confirm these findings,while removing potential confounding factors (populationsizes, densities and spatial distribution, variation in typeand timing of lockdowns, or noise in the data), weimplement a metapopulation SEIR model of COVID-19 driven by empirical mobility flows before and aftermitigation measures. The model uses a metapopulationframework, with S2 cells as geographical units connectedby the network of mobility flows before the initiation ofmitigation measures. We assign populations to S2 cellsin proportion to the sum of their out- and self-flows.Furthermore, we assume that flows represent primarilycommuting trips, and displacements outside the residentcells are followed by returns after a period of 8 hours.Previous research indicates that a substantial fraction ofresidents in areas as counties and municipality are notrepresented in commuting flows, and therefore we enforcethat only 40% of residents in each cell travel (inside orout) [42]. Cities in this idealized configuration maintaintheir empirical Φ, this design has the effect of scalingflows by a constant factor, without altering the networkstructure or the relative ranking of cell outflows.To produce instances of a single city with differentvalues of Φ , we reshuffle a portion of randomlyselected links by picking a new destination at randomwhile maintaining the link-weights. This procedurecreates multiple realizations of the city, preserving thepopulation distribution and densities, as well as the totalnumber of trips along with the number of destinationsper origin. To simulate the effect of lockdowns, wereplace the pre-lockdown empirical mobility network withthe post-lockdown version once the fraction of infectedindividuals in the population reaches a threshold P th .The mobility is reduced according to the empirical tripdecrease in every cell, and a fraction X S of susceptibleindividuals are considered as non-interacting [43–45].The parameter P th controls the time of the lockdown,while X S determines its severity. (See Methods fora detailed description of the model and the values ofrelevant epidemic parameters.)We begin by checking whether the model canreproduce the trend in Fig. 3 a . The equivalent plotfor three representative cities is shown in Fig. 4 a ,where we extract R eff from the incidence curves of thesimulations. The onset is set at 10 accumulated casesand h R early i is averaged over three weeks after onset, asdone for the empirical data. The R for each individualcity ranges from 0 . − .
97 indicating a clear signalfor the transmissibility increasing with centralization.When measuring the correlation for the three citiescollectively, confounding factors such as differences inpopulation density and mobility distributions emerge,and R decreases to 0 .
63 in order of magnitude agreementwith that seen for Fig. 3 a obtained aggregating 22different cities. Similar to that seen for Fig. 3 b , we alsoreproduce the observation of the peak incidence I max being monotonic in Φ as shown in Fig. 4 b . This isreflected in the final size of the outbreak (Fig. 4 c ) and thetime taken to reach the peak incidence (SupplementaryFigure 12), with more centralized cities experiencingstronger transmission, faster spread and wider prevalencein the population. These attributes in combinationcan rapidly overwhelm hospital capacity as well as theFIG. 3: Connecting hierarchy with epidemic features and mitigation efforts.
Shown are the top 22 UScities by number of counties with more than two million inhabitants until June 14, 2020. a Average R eff over threeweeks after the onset of 100 cases as a function of Φ. Initial transmission increases with centralization. b Accumulated number of new cases per capita two weeks before the maximum incidence I max . Cities in pale yellowhave already peaked, while infections continue to grow in those marked in red. The figure suggests the extent ofspread is strongly correlated with centralization. In c , Φ versus relative decrease in total flow. Mobility reductionsare much more drastic in centralized cities. d Synchronization of mobility reduction and contagion spread amongcity counties measured through the Pearson coefficient of plots as those shown in Fig. 2 g-i for Atlanta, Chicago andNYC. Response to mitigation is more sensitive in cities with higher Φ. (The equivalent figures for all 22 cities areshown in Supplementary Fig. 10). These results were obtained with data from the New York Times (SupplementaryTable 1). We show the equivalent plots using an alternative data source, USAFacts, in Supplementary Fig. 11.healthcare system at large, and is indeed what was seenin hierarchical cities such as NYC, London and Milan.On the other hand, Fig. 3 d suggests that citieswith higher Φ largely achieved a better reduction intransmission with lockdown measures. To simulate this,in Fig. 4 d we plot the final size of the pandemic byinstituting an 80% reduction in interactions ( X s = 0 . P th = 5 × − .Remarkably we see an inversion of the curve as comparedto Fig. 4 c with the trends now reversed; the final sizeof the pandemic is lower in cities with higher Φ andis decreased by an order of magnitude as compared to the scenario with no mitigation. The inversion of thecurve resulted from a rather strong lockdown, so inFig. 4 e we show the case for a softer lockdown with X s = 0 .
4; here we see the same trend with Φ as inthe case with no lockdown, however, the size of theoutbreak is reduced by a factor of five. In addition thetime taken to institute mobility restriction measures isa crucial parameter, and in Fig. 4 f , we show the casefor an earlier (but still soft) lockdown with X s = 0 . P th = 10 − , finding a further decrease by a factor of threein the pandemic size. In terms of assessing the effect ofdifferent flavors of lockdowns, the connection between theFIG. 4: Modeling disease spread by type of city.
Results of a metapopulation model using the S2 cells as basicgeographical units. Simulations are run in each city with different values of Φ, obtained by the randomizationprocedure described in the text. Each box reflects 100 runs and displays the median, quartiles, the 5% and 95%confidence intervals. In a , R eff in the early stages, averaged over three weeks after the onset of 10 cases as afunction of Φ, as in Fig. 3 a . The peak incidence I max is shown in b , and the final epidemic size in c both as afunction of Φ. All three panels correspond to the baseline mobility before lockdown. In d-f we show the pandemicsize for three different lockdown scenarios: a strong lockdown, X s = 0 .
8, for P th = 5 × − ; a soft lockdown, X s = 0 .
4, at the same prevalence, and finally a soft but earlier lockdown X S = 0 . P th = 10 − .size of the outbreak and its dependence on Φ, is in generala complex function of the epidemiological parameters,the extent of mobility reduction and the distribution offlows. In Supplementary Figs. 13-15, we explore aspectsof this interdependence for different values of R and X S ,confirming that when lockdown measures are enforced intime and in strength, centralized cities while being moresusceptible, outperform or do at least as well as sprawledcities in mitigating the outbreak.In summary, we studied how mobility restrictions in urban areas affect the propagation of an infectiousdisease. We leveraged a massive global dataset thatcaptures aggregate flows of populations around theglobe in a consistent way since pre-pandemic timesall the way to the most recent week. In a previouswork, we had shown that hierarchical cities have betterindicators in terms of the use of public transportation,walking, emissions per-capita and health indicators.However, their mobility structure favors spreading ofinfectious diseases in terms of speed and extent of thecontagions. At the same time, lockdown and travelrestriction measures can lead to better outcomes in morehierarchical cities. From a policy-making point of view,it seems prudent to deploy robust early warning systemswithin hierarchical cities in particular. Furthermore, it iseffective to enforce mitigation measures as early and asthoroughly as possible, given that the time-to-responseis particularly crucial in hierarchical cities within ornear an epidemic outbreak. Sprawled cities, with theirdistributed mobility and less connected outbreaks, havea larger window of time within which to enforce policymeasures, yet even so, the intensity of response isimportant to reduce the final number of cases. Thesefindings, while presented in the context of COVID-19,are also applicable to other potential infectious diseases.These results shed new light on the ongoing debate on thebest design for cities, balancing between the multipliereffects that lead to socio-economic development againsttheir susceptibility to threats such as pandemics. Methods
Mobility data sets.
The mobility flows aresourced from the Google COVID-19 AggregatedMobility Research Dataset, containing anonymized tripsaggregated over users who have turned on the LocationHistory setting, which is off by default. This is similarto the data used to show how busy certain types ofplaces are in Google Maps, helping identify when a localbusiness tends to be the most crowded. The datasetaggregates flows of populations between S2 cells ( https://github.com/google/s2geometry ) of approximately 5km . To produce this dataset, machine learning isapplied to logs data to automatically segment it intosemantic trips [35]. To provide strong privacy guarantees,all trips were anonymized and aggregated using adifferentially private mechanism [46] to aggregate flowsover time. This research is done on the resulting heavilyaggregated and differentially private data. No individualuser data was ever manually inspected, only heavilyaggregated flows of large populations were handled. Limitations.
The results should be interpreted inlight of several limitations. First, the Google mobilitydata is limited to smartphone users who have optedin to Googles Location History feature. These datamay not be representative of the population as whole,and furthermore their representativeness may vary bylocation. Importantly, these limited data are onlyviewed through the lens of differential privacy algorithms,specifically designed to protect user anonymity andobscure fine detail. Moreover, comparisons across ratherthan within locations are only descriptive since theseregions can differ in substantial ways.
Epidemic data sets.
The epidemic data has beendownloaded from sources listed in the Data Availabilitystatement and in Supplementary Table 1.
Mobility flows in urban areas.
The flows are incorporated in an Origin-Destination matrix T ( t ),whose elements T ij ( t ) encode the trip flow at week t between the two spatial units i and j . The diagonalterms T ii correspond to movements within the area. Thegeographical unit corresponds to S2 cells of 5 km . Thetotal flow of a territory is the sum of the trips over allthe S2 cells present in the city, T = P i,j T ij . In general,the relative trip-flow change between two timestamps t and t is calculated as ( T ( t ) − T ( t )) /T ( t ). Note thatwhen we estimate the reduction after lockdown, t refersto the mobility prior to the restrictions and t after thelockdown. Hierarchical structure of urban mobility.
Tocalculate Φ, a hotspot level is assigned to eachgeographical unit (S2 cells), using a recurrent Lorenzcurve as explained in Ref. [35]. Once every cell i isassigned a level L i , trip flows between cells are aggregatedas: S ‘m = P i 1) + δ ( ‘ − , m ) } . (2) Calculation of driving between incidence curves. In order to quantify the driving in the spreadingbetween different areas of a city, we calculated thetransfer entropy[47] between the time series of thedisease incidence at the county (borough) level for timewindows of increasing sizes. Starting from the firstreported case to the latest available data (in most cases,the first week of June 2020, see the SupplementaryInformation for details on the epidemiological data).For each time window, the driving each administrativeunit i had over the others is calculated as the averagetransfer entropy h TE i i = 1 /N P j TE ij between theincidence time series of unit i and all the other units j , with N the number of administrative units in thecity. The transfer entropy was evaluated using the RTransferEntropy library ( https://cran.r-project.org/web/packages/RTransferEntropy/vignettes/transfer-entropy.html ) in R, that also provides anestimation of the statistical significance of the results. SEIR metapopulation model. The model isstructured in a meta-population framework withSusceptible S, Exposed E, Infected I and RecoveredR compartments and taking as basic spatial units theS2 cells provided by the mobility data. The wholepopulation of the city P is distributed among the cells i ,according to p i = P ( P j T ij ) /T where the index j runsover all cells including i and T corresponds to the totaltrips of the city. In the model without travel restrictions,40% of the population of every cell i moves and selectstheir destination proportional to outflow T ij from i to theother cells j (including T ii ). The choice of a 40% mobilityhas been made in accordance with previous research,where it has been shown that for commuting flows, onlya fraction of the population actively moves[11, 42]. Alsonote that non-moving individuals are not excluded fromthe epidemic dynamics but interactions occur inside theircell of residence. To incorporate commuting flows insidethe epidemic dynamics, we followed a classical approachfor metapopulation models with recurrent mobility[11,42, 48]: introducing an effective force of infection forindividuals residing at cell j , defined as λ j . λ j accountsfor both the force of infection seen by an individual insidetheir residence cell λ jj and while commuting to other cells λ ji and can be calculated as λ j = λ jj σ j /τ + X i ∈ v ( j ) λ ji σ ji /τ σ j /τ (3)where σ j represents the travel rate of individuals in j , σ ji the travel rate between cells j and i while τ accountsfor the time usually spent outside the home cell during aworking day ( τ − ∼ / i of cell j , v ( j ). Finally, λ jj and λ ji arecalculated as: λ ji = βN ∗ j I ji + X l ∈ v ( j ) I lj S ji S i (4)where β is the per contact infection rate, N ∗ j is theeffective population of j having into account commutingand the subscripts in I ij (resp S ij ) refer to the infected(susceptible) visitors from i in j (for a detailed derivationof λ j and λ ji see section 4 . Effect of mobility restrictions and stay-at-homeorders. To model the effect of lockdowns on mobility,we need to consider that mobility flows change in bothmagnitude and destination in response to the restrictions.With reductions that can reach up to 80% reduction offlows compared to baseline levels. In the metapopulationmodel and for sake of simplicity, for each city only twomobility networks have been extracted from the GoogleCOVID-19 Aggregated Mobility Research Dataset: oneconsidering a typical day prior to restrictions T ij andanother after restrictions have been imposed, L ij . Thetotal trips per cell i are then T i = P j T ij and L i = P j L ij . As for the normal mobility regime, where weimpose that the 40% of population of each cell willmove with destinations proportional to T ij , during travelrestrictions we assume that flows and destinations arechosen according to the new mobility matrix L ij . Sincetravel flows in matrix L are usually smaller than flowsin T , the total reduction in mobility is L i /T i , with thefraction of individuals traveling in the system 0 . L i /T i ).In addition, it is important to note that duringstay-at-home orders part of the population remainedisolated or only interacted with individuals in their household; not participating in the global spreadingprocess directly. This effect has been modeled inthe literature [43–45] by including a fraction X S ofsusceptible individuals who do not participate in theinfection process. In the main text, X S is fixed at0 . e and f andin Supplementary Figs. 14-16. Finally, in order tomodel the fact that restrictive measures are enforcedwhen outbreaks are discovered in the city, we assumethat both travel restrictions and stay-at-home orders areimposed once the prevalence of the disease reached acertain threshold P th , equal for all the cities considered.Unless otherwise specified, the particular parametersselected for the model are: the infectivity per contact β = 0 . − , the average time spent as infectious t I = µ − = 3 . t E = 3 . Acknowledgments We thank Aaron Schneider, Aaron Stein, AhmedAktay, Alvin Raj, Amy Chung-Yu Chou, AndrewOplinger, Ashley Zlatinov , Blaise Aguera y Arcas,Bryant Gipson, Charina Chou, Christopher Pluntke,Damien Desfontaines, Eric Tholome, Ewa Dominowska,Gregor Rothfuss, Iz Conroy, Janel Thamkul, JanetWhiteman, Jason Freidenfelds, Jeff Dean, Karen LeeSmith, Katherine Chou, Leeron Morad, Lizzie Dorfman,Marlo McGriff, Mia Vu, Michael Howell, Paul Eastham,Rif Saurous, Rishi Bal, Royce Wilson, Ruth Alcantara,Shawn O’Banion, Stephanie Cason, Thomas Roessler,Vivien Hoang, Yanning Zhang, Xue Ben and BrianDickinson for their support and guidance.M.M. is funded by the Conselleria d’Innovaci´o,Recerca i Turisme of the Government of the BalearicIslands and the European Social Fund with grant codeFPI/2090/2018. J.A., M.M., S.M. and J.J.R. alsoacknowledge funding from the project Distancia-COVID(CSIC-COVID-19) of the CSIC funded by a contributionof AENA, from the Spanish Ministry of Science andInnovation, the AEI and FEDER (EU) under thegrant PACSS (RTI2018-093732-B-C22) and the Mariade Maeztu program for Units of Excellence in R&D(MDM-2017-0711). A.B. and V.N. acknowledge supportfrom the UK EPSRC New Investigator Award GrantNo. EP/S027920/1. GG, SH and SM acknowledgesupport from from NSF Grant IIS-2029095 and theUS Army Research Office under Agreement NumberW911NF-18-1-0421. A.K. is supported by the NationalDefense Science and Engineering Graduate Fellowshipthrough the Department of Defense. Author contributions G.G., S. Meloni, V.N., J.J.R. and A.S. developed theconcepts and designed the study. A.B., S.H., A.K., M.M.0and S. Mimar analyzed the data. A.S. computed andprovided the mobility map data. J.A., S. Meloni andJ.J.R. developed the model. J.A. performed the modelsimulations. G.G., M.M., S. Meloni, J.J.R. and A.S.contributed to the work methodology. G.G., M.M., S.Meloni, V.N. and J.J.R wrote the paper. G.G., S. Meloni,J.J.R. and A.S. coordinated the study. All authors read,edited, and approved the final version of the paper. Theauthors are listed in alphabetical order. Data and code availability statement The Google COVID-19 Aggregated Mobility ResearchDataset used for this study is available with permissionfrom Google LLC.Covid data sources:World: Italy: https://github.com/pcm-dpc/COVID-19 USA: New York Times https://github.com/nytimes/covid-19-data and USAFacts https://usafacts.org/visualizations/coronavirus-covid-19-spread-map/ Spain: https://github.com/montera34/escovid19data South Korea: India: The code to calculate the flow hierarchy in citiesis available in the following link: https://mygit.katolaz.net/aleix/flow-hierarchy . [1] A. Flahault and A.-J. Valleron, Mathematical PopulationStudies , 161 (1992).[2] R. F. Grais, J. H. Ellis, and G. E. 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Aguilar et al . 2 The city boundaries used throughout the study are the functional urban areas provided by the OECD https://ec.europa.eu/eurostat/statistics-explained/index.php/Glossary:Functional_urban_area . Country URL DescriptionWorld ecdc.europa.eu/en/publications-data/ European Centre forDisease Prevention and ControlItaly github.com/pcm-dpc/COVID-19 Protezione Civileofficial monitoring of Covid casesUSA github.com/nytimes/covid-19-data New York Times coverage ofcovid cases by countiesUSA-2 usafacts.org/visualizations/ USAFacts alternative coverage ofcoronavirus-covid-19-spread-map/ covid cases by countiesSpain github.com/montera34/escovid19data Independent coverageof covid casesSouth Korea kaggle.com/marcuswingen/ Official coverage from Korea Centers foranalysis-of-covid-19-data-from-south-korea Disease Control & PreventionIndia kaggle.com/sudalairajkumar/ Official coverage from Indian Ministry ofcovid19-in-india/data20 Health & Family WelfareSupplementary Table 1: Covid data sources. Impact of urban structure on COVID-19 spread. Aguilar et al . 3Countries Countries Countries CountriesAfghanistan Finland Luxembourg Saudi ArabiaAngola France Malaysia SenegalArgentina Gabon Mali SingaporeAustralia Georgia Malta SlovakiaAustria Germany Mauritius SloveniaBahrain Ghana Mexico South AfricaBangladesh Greece Moldova South KoreaBelarus Guatemala Mongolia SpainBelgium Haiti Morocco Sri LankaBolivia Honduras Myanmar SwedenBosnia and Herzegovina Hungary Netherlands SwitzerlandBrazil India New Zealand TaiwanBulgaria Indonesia Nicaragua TajikistanBurkina Faso Iraq Niger ThailandCambodia Ireland Nigeria TogoCameroon Israel Norway Trinidad and TobagoCanada Italy Oman TurkeyChile Jamaica Pakistan UgandaColombia Japan Panama UkraineCosta Rica Jordan Paraguay United Arab EmiratesCroatia Kazakhstan Peru United KingdomCzechia Kenya Philippines United Republic of TanzaniaDenmark Kuwait Poland United States of AmericaDominican Republic Kyrgyzstan Portugal UruguayEcuador Latvia Qatar VenezuelaEgypt Lebanon Romania VietnamEl Salvador Libya Russia YemenEstonia Lithuania Rwanda ZambiaSupplementary Table 2: Table of world countries considered in Figure 1. Impact of urban structure on COVID-19 spread. Aguilar et al . 4Province Province Province Province ProvinceAgrigento Catania La Spezia Pavia SiracusaAlessandria Catanzaro Latina Perugia SondrioAncona Chieti Lecce Pesaro e Urbino Sud SardegnaAosta Como Lecco Pescara TarantoArezzo Cosenza Livorno Piacenza TeramoAscoli Piceno Cremona Lodi Pisa TerniAsti Crotone Lucca Pistoia TorinoAvellino Cuneo Macerata Pordenone TrapaniBari Enna Mantova Potenza TrentoBarletta-Andria-Trani Fermo Massa-Carrara Prato TrevisoBelluno Ferrara Matera Ragusa TriesteBenevento Firenze Messina Ravenna UdineBergamo Foggia Milano Reggio di Calabria VareseBiella ForlâĂIJ-Cesena Modena Reggio nellâĂŹEmilia VeneziaBologna ForlÃň-Cesena Monza e della Brianza Rieti Verbano-Cusio-OssolaBolzano/Bozen Frosinone Napoli Rimini VercelliBrescia Genova Novara Roma VeronaBrindisi Gorizia Nuoro Rovigo Vibo ValentiaCagliari Grosseto Oristano Salerno VicenzaCaltanissetta Imperia Padova Sassari ViterboCampobasso Isernia Palermo SavonaCaserta LâĂŹAquila Parma SienaSupplementary Table 3: Table of Italian provinces considered in Figure 1. Provinces Provinces Provinces ProvincesA CoruÃśa Cantabria La Rioja SalamancaÃĄlava CastellÃşn Las Palmas Santa Cruz de TenerifeAlbacete Ceuta LeÃşn SegoviaAlicante Ciudad Real Lleida SevillaAlmerÃŋa CÃşrdoba Lugo SoriaAsturias Cuenca Madrid TarragonaÃĄvila Girona MÃąlaga TeruelBadajoz Granada Melilla ToledoBaleares Guadalajara Murcia ValenciaBarcelona GuipÞzcoa Navarra ValladolidBurgos Huelva Ourense VizcayaCÃąceres Huesca Palencia ZamoraCÃądiz JaÃľn Pontevedra ZaragozaSupplementary Table 4: Table of Spanish provinces considered in Figure 1. Provinces Provinces ProvincesBusan Gwangju Jeollabuk-doChungcheongbuk-do Gyeonggi-do Jeollanam-doChungcheongnam-do Gyeongsangbuk-do SejongDaegu Gyeongsangnam-do SeoulDaejeon Incheon UlsanGangwon-do Jeju-doSupplementary Table 5: Table of South Korean first-tier administrative divisions consideredin Figure 1. Impact of urban structure on COVID-19 spread. Aguilar et al . 5States States States StatesAndhra Pradesh Haryana Odisha UttarakhandAssam Jammu and Kashmir Punjab West BengalBihar Jharkhand RajasthanChandigarh Karnataka Tamil NaduChhattisgarh Kerala TelenganaDelhi Madhya Pradesh TripuraGujarat Maharashtra Uttar PradeshSupplementary Table 6: Table of Indian States considered in Figure 1. Cities Cities Cities CitiesAtlanta Hartford New Orleans San DiegoAustin Houston New York San FranciscoBoston Indianapolis Oklahoma SeattleCharlotte Jackson Orange St. LouisChicago Jacksonville Philadelphia TulsaCincinnati Jefferson Phoenix Virginia BeachColumbus Las Vegas Pima WakeCuyahoga Los Angeles Pittsburgh WashingtonDallas Memphis PortlandDavidson Miami RichmondDenver Milwaukee SacramentoDetroit Minneapolis Salt LakeFresno New Haven San AntonioSupplementary Table 7: Table of US cities considered in Figure 1. Impact of urban structure on COVID-19 spread. Aguilar et al . 6 - - 02 2020 - - 09 2020 - - 16 2020 - - 23 2020 - - 01 2020 - - 08 2020 - - 15 2020 - - 22 2020 - - 29 2020 - - 05 2020 - - 12 2020 - - 19 2020 - - 26 2020 - - 03 2020 - - 10 2020 - - 17 2020 - - 24 2020 - - 31 2020 - - T USA(a) New YorkLos AngelesChicagoDallasMiami San FranciscoHoustonAtlantaPhoenixPhiladelphia - - 02 2020 - - 09 2020 - - 16 2020 - - 23 2020 - - 01 2020 - - 08 2020 - - 15 2020 - - 22 2020 - - 29 2020 - - 05 2020 - - 12 2020 - - 19 2020 - - 26 2020 - - 03 2020 - - 10 2020 - - 17 2020 - - 24 2020 - - 31 2020 - - T (b)Spain MadridBarcelonaSevilleBilbaoZaragoza MalagaMurciaGranadaVigoPalma - - 02 2020 - - 09 2020 - - 16 2020 - - 23 2020 - - 01 2020 - - 08 2020 - - 15 2020 - - 22 2020 - - 29 2020 - - 05 2020 - - 12 2020 - - 19 2020 - - 26 2020 - - 03 2020 - - 10 2020 - - 17 2020 - - 24 2020 - - 31 2020 - - T (c)Italy MilanRomeNaplesTorinoFlorence SalernoPalermoCataniaGenoaBari - - 02 2020 - - 09 2020 - - 16 2020 - - 23 2020 - - 01 2020 - - 08 2020 - - 15 2020 - - 22 2020 - - 29 2020 - - 05 2020 - - 12 2020 - - 19 2020 - - 26 2020 - - 03 2020 - - 10 2020 - - 17 2020 - - 24 2020 - - 31 2020 - - T (d) SouthKorea SeoulBusanTaeguTaejonGwangju UlsanChonjuPohangChejuIksan - - 02 2020 - - 09 2020 - - 16 2020 - - 23 2020 - - 01 2020 - - 08 2020 - - 15 2020 - - 22 2020 - - 29 2020 - - 05 2020 - - 12 2020 - - 19 2020 - - 26 2020 - - 03 2020 - - 10 2020 - - 17 2020 - - 24 2020 - - 31 2020 - - T Sweden(e) GoteborgMalmoStockholm UppsalaVasteras - - 02 2020 - - 09 2020 - - 16 2020 - - 23 2020 - - 01 2020 - - 08 2020 - - 15 2020 - - 22 2020 - - 29 2020 - - 05 2020 - - 12 2020 - - 19 2020 - - 26 2020 - - 03 2020 - - 10 2020 - - 17 2020 - - 24 2020 - - 31 2020 - - T India(f) MumbaiKolkataDelhiMadrasBangalore HyderabadAhmedabadPuneSuratKanpur Supplementary Figure 1: Changes in mobility in 10 major cities of 6 countries that applieddifferent mitigation strategies . Curves in panels a-f represent temporal change in mobility comparedto the baseline average mobility in February.The reduction of mobility has an uneven impact across the different scales in a city. As we show inSupplementary Figure 2 for the United Kingdom, the longest trips beyond the city scale incur a moredrastic decrease in mobility, which can be observed in both the CCDF and the associated bar plot.Similar plots where the same trend can be observed are shown in Supplementary Figures 3 and 4 for theUnited States and Spain, respectively.a bSupplementary Figure 2: Reduction of mobility at different scales in the United Kingdom. a Complementary cumulative distribution of trip distances in 09-02-2020 and in 29-03-2020. b Percentageof change in total flow as a function of the distance of the trips.Impact of urban structure on COVID-19 spread. Aguilar et al . 7a bSupplementary Figure 3: Reduction of mobility at different scales in the United States ofAmerica. a Complementary cumulative distribution of trip distances in a 09-02-2020 and in 29-03-2020. b Percentage of change in total flow as a function of the distance of the trips.a bSupplementary Figure 4: Reduction of mobility at different scales in Spain. a Complementarycumulative distribution of trip distances in a 09-02-2020 and in 29-03-2020. b Percentage of change intotal flow as a function of the distance of the trips.Impact of urban structure on COVID-19 spread. Aguilar et al . 8 th case10 n e w c a s e s p e r w ee k p e r c a p i t a S w e d e n S o u t h K o r ea U S I n d i a Sp a i n I t a l y % D e c r e a s e i n M o b ili t y Supplementary Figure 5: Number of new cases per capita and mobility change in 6 countriesstarting from the week after th case. Curves are colored according to the percentage mobilitychange in each country relative to the week after reaching 100 cases.Impact of urban structure on COVID-19 spread. Aguilar et al . 9 N o r m a l i z e d F l o w Original HotspotsMean Week N o r m a l i z e d F l o w Weekly Hotspots ab Supplementary Figure 6: Flows to hotspots . a The normalized flow to inflow hotspots calculatedat the week of January 5 2020, over time, for the top 50 CBSAs in the US (only curves between .25and .5 shown, with the mean in gray.) We see that the epidemic conditions cause the flows to theoriginal hotspots to decrease, indicating a shift in travel destinations. b The normalized flow to hotspotscalculated at each week. We see that the flows increase, contrary to a , suggesting that people concentratetheir flows in different areas in response to the epidemic.Impact of urban structure on COVID-19 spread. Aguilar et al . 10 M i l w a u k ee - W a u k e s h a , W I R i v e r s i d e - S a n B e r n a r d i n o - O n t a r i o , C A I n d i a n a p o l i s - C a r m e l - A n d e r s o n , I N R i c h m o n d , V A O k l a h o m a C i t y , O K P h o e n i x - M e s a - C h a n d l e r , A Z V i r g i n i a B e a c h - N o r f o l k - N e w p o r t N e w s , V A - N C K a n s a s C i t y , M O - K S S a c r a m e n t o - R o s e v i ll e - F o l s o m , C A B a l t i m o r e - C o l u m b i a - T o w s o n , M D T a m p a - S t . P e t e r s b u r g - C l e a r w a t e r , F L C i n c i nn a t i , O H - K Y - I N H a r t f o r d - E a s t H a r t f o r d - M i dd l e t o w n , C T M i a m i - F o r t L a u d e r d a l e - P o m p a n o B e a c h , F L D a ll a s - F o r t W o r t h - A r l i n g t o n , T X S a n D i e g o - C h u l a V i s t a - C a r l s b a d , C A L o u i s v i ll e / J e ff e r s o n C o u n t y , K Y - I N J a c k s o n v i ll e , F L O r l a n d o - K i ss i mm ee - S a n f o r d , F L P r o v i d e n c e - W a r w i c k , R I - M A M e m p h i s , T N - M S - A R N a s h v i ll e - D a v i d s o n -- M u r f r ee s b o r o -- F r a n k l i n , T N B i r m i n g h a m - H oo v e r , A L L o s A n g e l e s - L o n g B e a c h - A n a h e i m , C A D e t r o i t - W a rr e n - D e a r b o r n , M I S t . L o u i s , M O - I L C h a r l o tt e - C o n c o r d - G a s t o n i a , N C - S C H o u s t o n - T h e W oo d l a n d s - S u g a r L a n d , T X D e n v e r - A u r o r a - L a k e w oo d , C O S a n A n t o n i o - N e w B r a u n f e l s , T X S a l t L a k e C i t y , U T R a l e i g h - C a r y , N C C l e v e l a n d - E l y r i a , O H A t l a n t a - S a n d y S p r i n g s - A l p h a r e tt a , G A B u ff a l o - C h ee k t o w a g a , N Y S a n J o s e - S u nn y v a l e - S a n t a C l a r a , C A S e a tt l e - T a c o m a - B e ll e v u e , W A M i nn e a p o l i s - S t . P a u l - B l oo m i n g t o n , M N - W I A u s t i n - R o u n d R o c k - G e o r g e t o w n , T X P i tt s b u r g h , P A S a n F r a n c i s c o - O a k l a n d - B e r k e l e y , C A P o r t l a n d - V a n c o u v e r - H i ll s b o r o , O R - W A L a s V e g a s - H e n d e r s o n - P a r a d i s e , N V C o l u m b u s , O H N e w Y o r k - N e w a r k - J e r s e y C i t y , N Y - N J - P A W a s h i n g t o n - A r l i n g t o n - A l e x a n d r i a , D C - V A - M D - W V N e w O r l e a n s - M e t a i r i e , L A P h i l a d e l p h i a - C a m d e n - W i l m i n g t o n , P A - N J - D E - M D B o s t o n - C a m b r i d g e - N e w t o n , M A - N H C h i c a g o - N a p e r v i ll e - E l g i n , I L - I N - W I F r a c t i o n a l C h a n g e Change in Average Hotspot Distance LowHigh Supplementary Figure 7: Distances between hotspots . Fractional change in average hotspot distancefrom the week of January 5 to the week of June 7 for the top 50 CBSAs in the US, colored by the hierarchyas of January 5.Impact of urban structure on COVID-19 spread. Aguilar et al . 11Supplementary Figure 8: Average Transfer Entropy h TE i for each administrative division(county or borough) with respect to the others as a function of time. Shown are six dif-ferent cities: Detroit, London, Madrid and Mexico city. Vertical red lines mark the date of the officiallockdown. For London the orange line marks an advisory from the Prime Minister’s office to suspend allnon essential activities, which occurred one week before the lockdown (red line).Impact of urban structure on COVID-19 spread. Aguilar et al . 12Supplementary Figure 9: Localization of flow in three cities with different mobility hierarchy. Flow distributions in the month of April in Atlanta, Chicago and New York are compared to the baselinemobility level in February. Cells with no flow change are colored grey and have mobility ratio 1. Mobilityincrease and decrease are illustrated by red and blue colors for cells with mobility ratio greater than andless than 1, respectively. Panels a, b, c represent self-flows, d, e, f represent in-flows, and g, h, i represent out-flows.Impact of urban structure on COVID-19 spread. Aguilar et al . 13Supplementary Figure 10: Reduction of R eff versus relative reduction of total flow at the countylevel in USA Metro Areas. R eff versus total flow reduction in counties within the same city, measuredfrom one week before the onset to three weeks after the onset. R eff is taken with one week of delay withrespect to mobility data. This data is used to measure the correlations shown in Figure 3 of the mainpaper. Only counties with more than 100 accumulated cases in the full observation period are shown.Impact of urban structure on COVID-19 spread. Aguilar et al . 14Supplementary Figure 11: Reproduction of Fig. 3 with alternative data. The same panels of theFig.3 of the main paper with data from USAFacts. a Average R eff over three weeks after the onset of 100cases as a function of Φ . Initial transmission increases with centralization. b Maximum incidence I max (infections per capita). Cities in pale yellow have already peaked, while infections continue to grow inthose marked in red. The figure suggests the extent of spread is strongly correlated with centralization.In d , synchronization of mobility reduction and contagion spread among city counties measured throughthe Pearson coefficient of plots as those in panels e-g , which reproduce those of shown in Fig. 2 g-i ofthe main manuscript for Atlanta, Chicago and NYC. The panel Fig.3 c is not reproduced because it isonly based on mobility data and it does not change with the source of the COVID-19 case information.Impact of urban structure on COVID-19 spread. Aguilar et al . 15 Supplementary Table 8: Table of US metro areas (and their short names) considered in Figure3 as function of Φ . Metro Area Shortening Φ Metro Area Shortening Φ New York (Greater) NYC 0.908 Dallas DAL 0.834Miami (Greater) MIA 0.876 Houston HOU 0.828Los Angeles (Greater) LA 0.874 Portland POR 0.826San Antonio SAT 0.873 Washington (Greater) WAS 0.824Boston BO 0.872 St. Louis SLS 0.809Chicago CHI 0.864 Pittsburgh PTB 0.803San Francisco (Greater) SF 0.860 Minneapolis MPL 0.796Denver DEN 0.850 Seattle STL 0.792Detroit (Greater) DET 0.849 Cincinnati CIN 0.790Philadelphia (Greater) PHI 0.848 Charlotte CHA 0.790Sacramento SAC 0.845 Atlanta ATL 0.788Supplementary Table 9: Table of counties per OCDE metropolitan area for New York City. County County County CountyBergen County Bronx County Essex County Hudson CountyHunterdon County Kings County Middlesex County Monmouth CountyMonroe County Morris County Nassau County New York CountyOcean County Orange County Passaic County Pike CountyPutnam County Queens County Richmond County Rockland CountySomerset County Suffolk County Sussex County Union CountyWarren County Westchester CountySupplementary Table 10: Table of counties per OCDE metropolitan area for Miami. County County County CountyBroward County Martin County Miami-Dade County Palm Beach CountySupplementary Table 11: Table of counties per OCDE metropolitan area for Los Angeles. County County County CountyLos Angeles County Orange County Riverside County San Bernardino CountySupplementary Table 12: Table of counties per OCDE metropolitan area for San Antonio. County County County CountyAtascosa County Bandera County Bexar County Comal CountyFrio County Guadalupe County Kendall County Medina CountyWilson CountyImpact of urban structure on COVID-19 spread. Aguilar et al . 16Supplementary Table 13: Table of counties per OCDE metropolitan area for Boston. County County County CountyEssex County Middlesex County Norfolk County Plymouth CountySuffolk CountySupplementary Table 14: Table of counties per OCDE metropolitan area for Chicago. County County County CountyCook County DeKalb County DuPage County Grundy CountyJasper County Kane County Kendall County Kenosha CountyLake County McHenry County Newton County Porter CountyWill CountySupplementary Table 15: Table of counties per OCDE metropolitan area for San Francisco. County County County CountyAlameda County Contra Costa County Marin County San Benito CountySan Francisco County San Mateo County Santa Clara CountySupplementary Table 16: Table of counties per OCDE metropolitan area for Denver. County County County CountyAdams County Arapahoe County Broomfield County Clear Creek CountyDenver County Douglas County Elbert County Gilpin CountyJefferson County Park CountySupplementary Table 17: Table of counties per OCDE metropolitan area for Detroit. County County County CountyLivingston County Macomb County Monroe County Oakland CountySt. Clair County Wayne CountySupplementary Table 18: Table of counties per OCDE metropolitan area for Philadelphia. County County County CountyBucks County Burlington County Camden County Cecil CountyChester County Delaware County Gloucester County Mercer CountyMontgomery County New Castle County Philadelphia County Salem CountySupplementary Table 19: Table of counties per OCDE metropolitan area for Sacramento. County County County CountyEl Dorado County Placer County Sacramento County Yolo CountyImpact of urban structure on COVID-19 spread. Aguilar et al . 17Supplementary Table 20: Table of counties per OCDE metropolitan area for Dallas. County County County CountyCollin County Cooke County Dallas County Denton CountyEllis County Fannin County Hood County Hunt CountyJohnson County Kaufman County Palo Pinto County Parker CountyRains County Rockwall County Somervell County Tarrant CountyVan Zandt County Wise CountySupplementary Table 21: Table of counties per OCDE metropolitan area for Houston. County County County CountyAustin County Brazoria County Chambers County Colorado CountyFort Bend County Galveston County Harris County Liberty CountyMontgomery County Polk County San Jacinto County Waller CountySupplementary Table 22: Table of counties per OCDE metropolitan area for Portland. County County County CountyClackamas County Clark County Columbia County Cowlitz CountyMultnomah County Skamania County Washington CountySupplementary Table 23: Table of counties per OCDE metropolitan area for Washington. County County County CountyAlexandria city Anne Arundel County Arlington County Baltimore CountyBaltimore city Calvert County Carroll County Charles CountyClarke County Culpeper County District of Columbia Fairfax CountyFalls Church city Fauquier County Frederick County Fredericksburg cityHarford County Howard County Jefferson County Loudoun CountyMontgomery County Prince George’s County Prince William County Rappahannock CountySpotsylvania County St. Mary’s County Stafford County Warren CountySupplementary Table 24: Table of counties per OCDE metropolitan area for St. Louis. County County County CountyJefferson County Jersey County Lincoln County Madison CountyMonroe County St. Charles County St. Clair County St. Louis CountySt. Louis city Warren CountySupplementary Table 25: Table of counties per OCDE metropolitan area for Pittsburgh. County County County CountyAllegheny County Washington County Westmoreland CountyImpact of urban structure on COVID-19 spread. Aguilar et al . 18Supplementary Table 26: Table of counties per OCDE metropolitan area for Minneapolis. County County County CountyAnoka County Carver County Chisago County Dakota CountyHennepin County Isanti County Kanabec County Pierce CountyRamsey County Scott County Sherburne County St. Croix CountyWashington County Wright CountySupplementary Table 27: Table of counties per OCDE metropolitan area for Seattle. County County County CountyKing County Pierce County Snohomish County Thurston CountySupplementary Table 28: Table of counties per OCDE metropolitan area for Cincinnati. County County County CountyBoone County Bracken County Butler County Campbell CountyClermont County Dearborn County Gallatin County Grant CountyHamilton County Kenton County Ohio County Pendleton CountyWarren CountySupplementary Table 29: Table of counties per OCDE metropolitan area for Charlotte. County County County CountyCabarrus County Gaston County Mecklenburg County Union CountyYork CountySupplementary Table 30: Table of counties per OCDE metropolitan area for Atlanta. County County County CountyBarrow County Bartow County Butts County Cherokee CountyClayton County Cobb County Coweta County Dawson CountyDeKalb County Douglas County Fayette County Forsyth CountyFulton County Gwinnett County Henry County Newton CountyPaulding County Rockdale County Walton CountyImpact of urban structure on COVID-19 spread. Aguilar et al . 19 t ( I m a x ) AtlantaBostonWashington Supplementary Figure 12: Relation between the time of the incidence peak and Φ . Simulationswithout lockdown and with the same parameters as in Fig. 4 of the main manuscript. The morehierarchical cities are, higher Φ , the quicker the peak arrives. a bc d no lockdown no lockdownno lockdown with lockdown Supplementary Figure 13: Model with R ≈ . . Simulations run with the same parameters as Fig.4 of the main manuscript but decreasing the infectivity parameter β to obtain a reproduction number R ≈ . . The panels without lockdown are: a the height of the peak of incidence, b the time of thepeak and c the epidemic size, all as a function of Φ . In d , the epidemic size versus Φ for a simulationwith lockdown X S = 0 . and triggering the lockdown at a prevalence P th = 5 × − .Impact of urban structure on COVID-19 spread. Aguilar et al . 20 F i n a l S i z e Supplementary Figure 14: Model with R ≈ . . Simulations run with the same parameters as Fig.4 but with β = 0 . days − inducing a reproduction number R ≈ . for a city generated with themobility network and total population of the Atlanta metropolitan area. The value of the epidemic sizeis explored as a function of Φ for different values of X S that are shown in the legend. In this way,it is possible to observe the inversion of the size versus Φ curves for strong lockdowns. Given the lowinfectivity in this figure P th = 10 − . F i n a l S i z e Supplementary Figure 15: Model with R ≈ . . Simulations run with the same parameters as Fig.4 ( β = 0 . days − ) producing a reproduction number R ≈ . for a city generated with the mobilitynetwork and total population of the Atlanta metropolitan area. The value of the epidemic size is exploredas a function of Φ for different values of X S that are shown in the legend. In this way, it is possible toobserve the inversion of the size versus Φ curves for strong lockdowns. As most of the panels of Figure4, P th = 5 × − .Impact of urban structure on COVID-19 spread. Aguilar et al . 21 F i n a l S i z e Supplementary Figure 16: Model with R ≈ . . Simulations run with the same parameters as Fig.4 but with β = 0 . days − inducing a reproduction number R ≈ . for a city generated with themobility network and total population of the Atlanta metropolitan area. The value of the epidemic sizeis explored as a function of Φ for different values of X S that are shown in the legend. In this way, it ispossible to observe the inversion of the size versus Φ curves for strong lockdowns. As most of the panelsof Figure 4, P th = 5 × −3