弱連接理論新洞察：長(zhǎng)程強(qiáng)邊提升城市治理能力 Strong long ties facilitate epidemic containment on mobility networks

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PNASNexus,2024,3,pgae515

eUS

/10.1093/pnasnexus/pgae515

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ResearchReport

Stronglongtiesfacilitateepidemiccontainmentonmobilitynetworks

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JianhongMou

o

a

,1,SuoyiTan

a

,1,JuanjuanZhang

b

,

c

,1,BinSai

a

,MengningWang

a

,BitaoDai

a

,Bo-WenMing

o

b

,ShanLiu

d

,

ZhenJine

,GuiquanSun

e

,f

,HongjieYu

b

,

c

,g

,*

andXinLu

a

,

*

a

CollegeofSystemsEngineering,NationalUniversityofDefenseTechnology,Changsha410073,China

b

DepartmentofEpidemiology,SchoolofPublicHealth,KeyLaboratoryofPublicHealthSafety,MinistryofEducation,FudanUniversity,Shanghai200032,China

c

ShanghaiInstituteofInfectiousDiseaseandBiosecurity,FudanUniversity,Shanghai200032,China

d

SchoolofManagement,Xi’anJiaotongUniversity,Xi’an710049,China

e

ComplexSystemsResearchCenter,ShanxiUniversity,Taiyuan030006,Shanxi,China

f

DepartmentofMathematics,NorthUniversityofChina,Taiyuan030051,Shanxi,China

g

DepartmentofInfectiousDiseases,HuashanHospital,FudanUniversity,Shanghai200032,China

*Towhomcorrespondenceshouldbeaddressed:Email:

xin.lu.lab@

(X.L.);Email:

yhj@

(H.Y.)1J.M.,S.T.,andJ.Z.contributedequallytothiswork.

EditedByMatjazPerc

Abstract

Theanalysisofconnectionstrengthsanddistancesinthemobilitynetworkispivotalfordelineatingcriticalpathways,particularlyinthecontextofepidemicpropagation.Localconnectionsthatlinkproximatedistrictstypicallyexhibitstrongweights.However,tiesthatbridgedistantregionswithhighlevelsofinteractionintensity,termedstronglong(SL)ties,warrantincreasedscrutinyduetotheirpotentialtofostersatelliteepidemicclustersandextendthedurationofpandemics.Inthisstudy,SLtiesareidentifiedasoutliersonthejointdistributionofdistanceandflowinthemobilitynetworkofShanghaiconstructedfrom1km×1kmhigh-resolutionmobilitydata.Weproposeagrid-jointisolationstrategyalongsideareaction–diffusiontransmissionmodeltoassesstheimpactofSLtiesonepidemicpropagation.ThefindingsindicatethatregionsconnectedbySLtiesexhibitasmallspatialautocorrelationanddisplayatemporalsimilaritypatternindiseasetransmission.Grid-jointisolationbasedonSLtiesreducescumulativeinfectionsbyanaverageof17.1%comparedwithothertypesofties.Thisworkhighlightsthenecessityofidentifyingandtargetingpotentiallyinfectedremoteareasforspatiallyfocusedinterventions,therebyenrichingourcomprehensionandmanagementofepidemicdynamics.

Keywords:stronglongties,epidemiccontainment,mobilitynetworks,reaction–diffusiontransmissionmodel,grid-jointisolationstrategy

SignificanceStatement

Thisstudyilluminatesthedifferentiationbetweenthestrengthandlengthofconnectionsonmobilitynetworks.Ourresearchrevealsthatconnectionsbridgingdistantregionswithhighinteractionintensity,termedstronglong(SL)ties,exhibitlowspatialautocorrel-ationanddisplayatemporalsimilaritypatternindiseasetransmission,potentiallyfosteringsatelliteepidemicclustersandextendingthedurationofpandemics.Thesuperiorityofgrid-jointisolationstrategybasedonSLtiessuggeststhattheadoptionofadvancedisolationstrategiestargetingremotegrids,whichmaintainhigh-flowconnectionstoinfectedgrids,isimperativefortheformulationofeffectivepolicies.OurworkprovidesdifferentperspectivesforassessingtheroleofSLtiesinnetworkdynamics,deepeningourcomprehensionofvariousrealms,includingeconomics,social,andbiologicalsystems.

Introduction

Althoughtiesserveascrucialchannelsinepidemicspreading,theirimpactsvarydependingonthetypeoftiesinvolved,includ-ingpositiveandnegativeedgesonsignednetworks(

1

),andinter-communitylinksoncommunity-relatednetworks(

2

).Moreover,severalstudieshighlightthedecisiveroleofintensityinshapingepidemicpropagationinmobilitynetworks(

3

,

4

).Researchacrossvariousdisciplineshasextensivelyexaminedtheimpactsoflong

ties(LG),focusingontheirspatialextent(

5

–

7

)andtierange(

8

,

9

).ThesestudiescollectivelyhighlightthefundamentalroleofLGinbridgingcrucialstructuresacrossvariousnetworks.LGserveascriticalchannelsfortherapiddisseminationofnovelinformationandthespreadofcontagiousbehaviors,underscoringtheirsignifi-canceinunderstandingandmanagingthedynamicsofsocial(

10

),biological(

11

),andepidemiologicalphenomena(

12

–

15)

.Inthecon-textofhumanmobility,infectiousdiseasesfrequentlytranscend

CompetingInterest:H.Y.hasreceivedresearchfundingfromSanofiPasteur,GlaxoSmithKline,YichangHECChangjiangPharmaceuticalCompany,ShanghaiRochePharmaceuticalCompany,andSINOVACBiotechLtd.Noneofthisfundingisrelatedtothisresearch.Alloth-erauthorsdeclarenocompetinginterests.

Received:August9,2024.Accepted:October28,2024

?TheAuthor(s)2024.PublishedbyOxfordUniversityPressonbehalfofNationalAcademyofSciences.ThisisanOpenAccessarticle

distributedunderthetermsoftheCreativeCommonsAttributionLicense(

/licenses/by/4.0/

),whichpermitsunrestrictedreuse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.

2|PNASNexus,2024,Vol.3,No.11

localizedgeographicalregions,spreadingrapidlyacrosscoun-triesandcontinents.Thisproliferationislargelyfacilitatedbythemovementofinfectedindividualsoverlargespatialscales(

4

,

16

–

18

).Suchlong-distancedispersalisgenerallyanticipatedtoacceleratetheviralspreadwithinanextensivepopulation(

19

).Onceaninfectedindividualtravelsfromtheprimaryout-breakspottoanunaffectedremoteone,ittriggerstheemergenceofanewinfectioussubpopulation,knownasasatellitecluster.Thesenascentclusterscansubsequentlyexpand,potentiallyservingasthesourceforfurtherlong-distancespreadofthedis-ease.Thelimitedoverlapbetweentheinitialoutbreakandsatel-liteclustersoftenresultsinmoreextensiveinfectionsacrossawiderspatialscope.

LGareoftenstructurallycategorizedasweakties(

20

–

22

),pro-vidinguniqueinformationalbenefitsnotreadilyavailablethroughclosercontacts

(23

–

25

).Strongties(ST),regardingthetopologicalproximityofassociatednodes,aretheoreticallyproventofacili-tatetheepidemicprevalence(

3

).However,theirsignificanceinmobilitycontexts,particularlyinurbanenvironments,necessi-tatesareevaluationoftheirperceivedweaknessandadistinctionbetweenthelengthandstrengthofties

(26

).Highmobilityacrossdistantlocationsfacilitatedbypoint-to-pointtransportationunderscoresthesignificanceofthesetiesoverextendedspans

(27

,

28

).Ithasbeenhighlyrecommendedthatthesetravelsbere-tainedasmuchaspossibletoextractspatialnetworkstructurefromlarge-scaleorigin–destinationflowdata(

29)

.Notably,insomeinstances,hightrafficvolumesonlong-distanceroutes,suchasthoseconnectingairportsandrailstations,surpassthoseofnearbytravel.Theefficacyofpublictransportationshutdowns,specificallylong-distancebuses,inmitigatingthespreadofacity-wideepidemic

(30

),underscoresthepivotalroleoflong-distancetiescharacterizedbysignificantmobility,referredtoasstronglong(SL)ties.Severingthesetiesaidsincontainingdiseaseswithinlocalizedareas,therebyacceleratingepidemicextinction,espe-ciallywhendetailedtrajectoriesofinfectedindividualsareun-known.Mobiledevicedata,especiallyderivedfromcalldetailrecords(

31

–

33

),facilitatestheidentificationofSLtiesandaidsinunderstandingepidemicpropagationonacitywidescale.However,amajorityofstudies(

34

,

35

)employmobilitydatawithlowspatialresolution,rangingfromafewtodozensofkilo-meters,limitingthein-depthinvestigationneededtodistinguishthelengthandstrengthofmobilityties.

Numerousresearchershaveconfirmedtheeffectivenessofnonpharmaceuticalinterventions(NPIs)incontrollingthespreadofphysical-contactdiseases,includingsocialnetwork-baseddis-tancing

(36

),contacttracing

(37

),citywidelockdown(

38

),andetal.Theimpactofcommunitystructureonepidemicsoffersvaluableinsightsforpreventingdiseasespreadbetweencommu-nitiesbychangingthestructureofthecontactnetworkthroughNPIs

(39

,

40

).Inter-communityties,oneofthetypesofLG,playacrucialroleinepidemiccontrolfortheprofoundimpactofcom-munitystructureonnetworkdynamics,yieldingtheoutperform-anceofimmunizinginterventionstargetedatindividualsbridgingcommunitiescomparedwiththosetargetinghighlyconnectedin-dividuals(

40

).However,theseapproachesmayunderestimatetheriskposedbyunconfirmedinfectedindividualstravelingtodis-tantdistricts,whichcouldpotentiallyfacilitatefurthertransmis-sion.ThestrengthofLGisalsovital,becauseitservesasacriticalindicatorforidentifyingremoteareaswhereunconfirmedin-fectedindividualsmightbelocated,therebyaidinginthepre-emptivecontainmentofpotentialinfectionhotspots.Despiteitssignificance,limitedresearchhasbeenconductedonthestrengthofLG,particularlyindifferentiatingbetweenLGandSLties,

letalonethequantificationandidentificationofSLties.Additionally,itremainsuncertainwhetherthevitalityofgridsconnectedtotheinitialoutbreakviaSLtiesexceedsthatofgridsconnectedbyothertypesofties.Thisraisesacriticaldecisionpointforpolicymakers:whetherlimitingrestrictionstogeograph-icalneighboringareassuffices,orifitisnecessarytoexpandcon-tainmenteffortstoremoteregionsconnectedbySLties.Thisuncertaintyunderscorestheneedforanuancedanalysisofhu-manmobilitypatternsandtheirinfluenceondiseasespread.

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Thisworkemphasizesconnectionsthatpossessbothspatialandsocialcharacteristics,takingintoaccountthespatialheterogeneityoftheintensitydistribution,ratherthanfocusingsolelyonsingleattributesliketheedgepositionorsignedattributes.WealsointendtothoroughlyevaluatethesignificanceofSLtiesinidentifyingpo-tentiallyhazardousareas.Specifically,gridsconnectedbySLtiestotheinitialoutbreaksitearemorelikelytoformsatelliteclusters,giventhepositivecorrelationbetweentransmissionprobabilityandpopulationflow.Initially,wequantifyandcharacterizeSLtiesforeach1km×1kmgridinShanghaibyaggregatingdistanceandpopulationflowfromhigh-resolutioncellularsignalingdata(CSD).Weproposeagrid-jointisolationstrategythatsupportspre-emptivequarantineforunconfirmedgridsreceivingindividualsfromconfirmedones,inwhichareaction–diffusiontransmission(RDT)modelisestablishedtosimulatethespreadoftheOmicronvariantofSARS-CoV-2crossgridsinShanghai.Thisstrategyfacili-tatesquantifyingtheeffectivenessofSLtiesinidentifyingpotentialhigh-riskgridscomparedwithtiesdefinedbyothercriteria:thosewiththehighestflow(ST),thegreatestdistance(LG),andtheshort-estdistance(shortties,SH).

Results

Statisticalandspatialfeaturesofties

Theoverviewofmobilitypatternsduringthreephases(seeFig.

1

AandTable

S1

),segmentedaccordingtotheinterventionstringency(seeMaterialsandmethodsfordetails),illustratestheprevalenceoflong-distanceconnectionswithheavyflow,i.e.SLs.ThistypeoftieisquantitativelyidentifiedasoutliersusingDBSCANwithabaselineofdistancelargerthan10km(d>10,000)andflowgreat-erthan28(f>28)(seeMaterialsandmethodsfordetails).Theflowofconnectionsreferstothenumberofindividualstravelingthroughduringthespecificphase.

TodifferentiatethecharacteristicsofSLsfromSTs,LGs,andSHs,wedefineafixednumberofties,k,asthatofSLsforeachgrid.Specifically,werespectivelyextracttiescharacterizedbythetop-kmaximumflow,maximumdistance,andminimumdis-tance.AsshowninFig.

1

B,duringtheprelockdownphase(2022March1–31),23.68and9.41%ofSTsarealsoSHsandSLs,respect-ively,whereasonly0.19%ofSLsareidentifiedasLGs.Statistically,STspredominantlyconcentrateongridpairswithaveragedis-

--

tanced=5,656.93andaverageflowf=810.65,withoutliersatlongdistances.SLsconcentrateonoutlierswitharelativelynar-rowflowdistribution.LGs,coveringdistancesfrom50to100km,typicallydemonstrateflowsunder200.Conversely,SHs,exclud-ingself-connections,focusonlocalconnectionswithina10km

-

radius,withanaverageflowf=404.92(seeFig.

S3

).SHsandSTssignificantlyoverlapbecauseshort-distancetiestendtogenerateheavyflow.STsandSLsshowminoroverlapsinceseverallong-distancetiesaccommodatelargerpopulationsthantheirshort-distancecounterparts.

Spatially,thesefourtypesoftiescanbedistinguishedthroughspatialautocorrelation,quantifiedbytheglobalMoran’sindexη,whichmeasuresthesimilarityofincomingconnectionsamong

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Fig.1.Statisticalandspatialcharacteristicsofvarioustypesofties.Althoughdifferenttypesoftiesshareseveralconnections,theyshowvarious

statisticalandspatialcharacteristics.A)Theoverviewsofmobilitypatternsduringthreephasesareillustrated.B)Thejointdistributionofflow(f)anddistance(d)forvarioustypesoftiesduringtheprelockdownphasewithanexampleofgrid8,315isshown.Thenumberofalltypesoftiesforeachgrid

keepsinlinewiththatofSLs.φisthenumberofSLsduringthesecondphaseandκ-SLrepresentsthenumberofoverlappingtiesbetweenSTsandSLs.

C)ThespatialdistributionofSHs,LGs,STs,andSLsalongwithMoran’sindicesη.Linewidthrepresentsthestrengthoftheconnectionisexhibited.

neighboringgrids(see

SupplementaryNoteS1

).Theincomingconnectionsofgridsrefertothepossibilitybeingpassivelyiso-latedimposedbytheinfectedneighbors,andtheautocorrelationishighlyrelatedtotheoverlapofneighborsforallnodes.SLsshowthelowestspatialautocorrelation,withanaverageMoran’sindexη-sl=0.0974acrossthreephases.GridslinkedbySHsdisplayaspa-tiallyclustereddistribution,resultinginthehighestaverageauto-correlationη-sh=0.5615,followedbySTsandLGswithη-st=0.2536andη-lg=0.1935,respectively(seeTable

S2

).Allspatialautocorre-lationsarestatisticallysignificantwithP-value<0.001.GridsconnectedbySLsarerandomlydistributedwithoutsignificantclustering,whereasSHsconnectspatiallyproximategrids,showingsimilarincomingconnections.Peripheralgridscon-nectedbyLGsshowsignificantclustering,butgridsoutsidetheseclustersarescattered,therebyreducingspatialautocor-relation(seeFigs.

1

C,

S4,andS5

).

Epidemictemporalsimilarityamonggrids

Mostgridsshowatemporalcorrelationduringepidemicpropaga-tion,indicatingthatgridpairsmaybecomeinfectedwithinashorttime.Identifyingthesegridpairsandseveringtheirconnectioncanbeinstrumentalinreducingthehighlydynamiccorrelation,therebyslowingdiseasetransmission.ThelengthofSLsiscrucialinfacilitatingthespreadoftheepidemicbetweendistantgrid

pairs.Thestrengthoftheseconnectionsreflectsthetemporalconcordanceofarrivaltimesbetweensuchgridpairs,astheprob-abilityoftransmissionbetweengridsiscontingentuponthepopu-lationflow.Thisstudyinvestigatesthevariationinarrivaltimesbetweengridpairstoevaluatethetemporalsimilaritiesinepi-demicspread.Tofigureouttherelationshipbetweenhumanmo-bilityandtemporalsimilarity,i.e.whetherthetemporalsimilarityiscausedbypreviousorcurrenthumanmobility,weexaminethegapofarrivaltimesduringtheprelockdownandlockdown(2022April1–2022May30)phasesforgridpairsconnectedbytiesinthepreviousstages:thepreoutbreak(2022February15–28)andprelockdownphases,denotedasg1?2andg2?3,respectively.Thediscrepancieswithinthesamestagesarealsodiscussed,denoted

asg2?2andg3?3(seeFig.

2

A).Specifically,gx?yisthesetofg?yover-

allconnectionsundertheconsideredphases,i.e.gx?y={g?y},

whereg?y=|t?t|,(i,j)∈Exandtrepresentsthearrivaltime

ofgridiwhichisinfectedwithinthephasey,anddenotesthedif-ferenttypesoftiesduringphasex.

ThefindingssuggestthatSLseffectivelyidentifygridswithsubstantialflowacrossextensivespatialdistancesandpreservethetemporalconcordanceofgridpairs,akintoSTsandSHs(seeFig.

2

B).Specifically,SLscapture,onaverage,71.77and61.39%ofgridpairswithanarrivaltimegapof<7days,comparedwithSTswithinthecurrentandpreviousphases,respectively(seeTable

S3)

.Theincreasingnumberofgridpairswithg1?2≤7and

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Fig.2.Theeffectofdifferenttypesoftiesoncapturingtemporarilyhighlyrelatedgrids.SLeffectivelyidentifiesgridswithsubstantialflowacross

extensivespatialdistancesandpreservesthetemporalconcordanceofgridpairs.A)Thespatialdistributionofarrivaltimeduringtheprelockdownphaseforgridpairsconnectedbyvarioustypesoftiesinthesamephaseisexemplified.Thelinewidthofconnectionsonthetopmobilitynetworkrepresentsthepopulationflow,andthecolorofgridsonthebottommapdenotesthearrivaltime.B)Thestatisticaldistributionofthegapofarrivaltimebetweengridpairs,denotedasg,withinsetsdisplayingthecumulativehistogramsforeachtypeoftiesintheunitof7daysisindicated.Noticeably,thenonsignificantmobilityvariationbetweenthepreoutbreakandprelockdownphasesbringsinasimilardistributionbetweeng1-2andg2-2,andthecitywideepidemicpropagationduringtheprelockdownphasecausestheconcentrationofg2-3andg3-3.

g2-3≤7comparedwiththosewithg2-2≤7andg3-3≤7supportstheguidingeffectofpreviousmobilityonepidemictemporalsimilarity.Temporallysimilarandspatiallyremotegridsfromtheinitialoutbreaksitesignificantlyaccelerateepidemicpropa-gation,astheygetinfectedquicklyandtriggerfurtherepidemicexpansionwithlittleoverlapwiththeinitialone.Thisunder-scorestheimportanceofimplementingpreemptivequarantinemeasuresongridsconnectedtotheinitialoutbreakgridbySLstomitigateepidemicpropagation.

Epidemicpropagationcontainmentbasedongrid-jointisolationstrategy

TheabilityofSLstoidentifyremotegridpairswithhightemporalsimilarityhighlightsthepotentialeffectivenessofpreemptivelyisolatingneighboringgridsconnectedbytheseties,asdescribedbythegrid-jointisolatedstrategyinthiswork(seeFig.

3

AandMaterialsandmethods).Thisstrategysupportssimultaneouspre-emptiveisolationofneighbors(passiveisolation)ofgridsthatareconfirmedinfectiousanddirectlyisolated(activeisolation).The

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Fig.3.TheeffectofSLtiesonreducingcontagions.Grid-jointisolationbasedonSLsslowsdownepidemicpropagationforitspositiveeffectonisolatingremotesatelliteclusters.A)Thegeneralframeworkofgrid-jointisolationisdisplayed.Theinitialinfectiousgridswillbeactivelyisolatedifinfectionssurpassthethresholdα,andtheunconfirmedgrids(stars)pointedbyotheractivelyisolatedgirdswithtieset(dashedline)willbepassivelyisolatedwiththeeliminationofrelatedconnections.Squaresrepresentunconfirmedgrids,i.e.girdswithpatients<α.Theepidemicpropagationacrossspatial

networksisruledbytheRDT.B)TheschematicillustrationoftheRDTmodelwhereindividualschangetheirstatesaccordingtotheSEIRmechanismwithineachgridanddiffusebetweengridssubjecttothepopulationflowisshown.CirclesandsquaresrespectivelydenotethemovableandimmovableindividualswithS,E,I,andRstates,differentiatingwithdifferentcolors.C)TheperformanceofSLsinreducingthecumulativeinfections(Ic)alongwiththecorrespondingnumberofisolatedgrids(G),restrictededges(E),andquarantinedpopulation(P)isillustrated.Resultsareaveragedover50

independentrealizations.rG,rE,andrP,respectivelydenotestherelativeimprovementcomparedwithNUintermsofisolatedgrids,restrictededges,andquarantinedpopulation.D)Theepidemicarrivaltimeofeachgridaftergrid-jointisolationthroughvarioustypesofties,wherecirclesindicatesatelliteclustersisexhibited.Thenumberofuninfectedgridsforeachstrategy(Nun)isgiven.

infectiousgridsareconfirmedoncethenumberofpatientsexceedsacertainthresholdα.Specifically,thethresholdαrep-resentsthecriterionofisolatinggrids,thusdescribingthestrictnessofepidemiccontrolforeachgrid.TheRDTmodel(Fig.

3

BandseeMaterialsandmethods)simulatesepidemicpropagationacrossgridsduringgrid-jointisolationwiththegoodnessoffitequaling0.93,asvalidatedinFig.

S6

.Tominim-izetheimpactofinfectiondynamicsongridsnotlinkedtoSLs,wedevelopedanewmobilitynetworkcomprising4,358SL-relatedgridsandtheircorresponding6,172,854populationflows.Additionally,toevaluatetherelativeeffectivenessofdifferenttietypesinreducinginfections,westandardizedthenumberofcontrollableneighborsforeachgridtomatchtheSLscenario.Inthissection,wealsoconsidergrid-jointisolationaccordingtotheinfectionpressure(PR)ofgridswhichdescribestheprob-abilityofthegridbeinginfected(see

SupplementaryNoteS2

fordetails).ThestrategyofpassivelyisolatinggridslinkedbySLsresultsinarelativereductionincumulativeinfectionsbyaverage17.1%,i.e.(Rd〉=0.171,comparedwithothertypesofties,andanevengreaterreduction,Rd=0.196,comparedwithanullmodel(NU)thatonlyisolatesconfirmedgrids(seeTable

S4

andFig.

3

C).Notably,althoughtheSL-basedisolationstrategybringsinmoreisolatedgridsandrestrictedroutinescomparedwithothertypesofties,ityieldslessquarantinedin-dividualsthanSH,ST,andPR.

Simulationsinvolvinggrid-jointisolationthroughalltypesofties,exceptSLs,revealtheemergenceofseveralsignificantre-motesatelliteclustersthatareinfectedearly(seeFig.

3

D).Theseclustersactasnewsourcesofoutbreak,acceleratingthespreadoftheepidemic.Inaddition,SL-basedgrid-jointisolationyieldsasimilarnumberofuninfectedgridscomparedwithothertypesofties,exceptforLGs.SincegridsrelatedtoLGareusuallythecityperipheriesthataretypicallyinfectedlately,theyareoftenpassivelyisolatedatthetimeearlierthanthepossibleinfectedtimes,thusincreasingtheisolationofuninfectedgrids.Itisnote-worthythatsimulationunderSTsyieldsfewergridswithinashortarrivaltimethanSLs.Specifically,theST-focusedisolationstrat-egyleadsto853gridswithanarrivaltimeof<14days,whichisfewerthanthatachievedthroughSL-orientedisolation,andsig-nificantlylessthanthe1,324gridsobservedintheNUscenario(seeFig.

S7

).ToexplainthediscrepancybetweenthecumulativeinfectionsandthearrivaltimeassociatedwithSLs,weexaminethedynamicsofdailyconfirmedinfectionsunderdifferentcontrolmeasures(seeFig.

S8

).InthecontextofSTs,severalgridswithar-rivaltimesmallerthan14daysareidentifiedassatelliteseedsandinitiatenewoutbreaks,raisingthenumberofgridswithanarrivaltimeof25–34days.ThereactionprocessoftheRDTmodelwithinthesegridsinducesincreasinginfectionsafterseveraldays.Consequently,satelliteclustersbecomeprimarydriversofsec-ondarypropagation,leadingtoheavydailyconfirmedinfections.

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Fromtheperspectiveofcommunitystructureinmobilitynet-works,SLscapturemoreinter-communitylinksthanSTsandSHs,therebyisolatingmoregridswithdiversetopologicalfeaturesunderthejoint-gridisolationstrategy.AlthoughLGsconnectgridsacrossdifferentcommunities,mostpassivelyisolatedgridsarelocatedatcityperipherieswithoutanypatients,thusdimin-ishingtheeffectivenessofpassiveisolation(see

Supplementary

NoteS3

andFig.

S1

).

EffectiveinterventionofSLties

Thedeepanalysisofwhathappenedduringthegrid-jointisola-tionprocessfacilitatesacomprehensiveunderstandingoftheper-formanceofvarioustypesofties.Sinceactivelyisolatedgridsmaysimultaneouslyoptforpassiveisolationoftheirsharedneighbor-inggrids,thegrid-jointisolationstrategyfavorsgridpairswithfewcommonneighbors.ThesmallspatialautocorrelationofSLex-plainsthesignificantsuperiorityofcapturingmorepassiveisola-tion.Consideringthepassiveisolationofgridswithpatientslargerthanαsincetheyarepointedbyotheractivelyisolatedgrids,i.e.activeandpassiveisolatedgrids,SLandPRfacilitatetheidentifi-cationofhighlyhazardousgrids(seeFig.

4

A).

SLstendtopassivelyisolatesparselydistributedgridsduetotheirlowspatialautocorrelation,whereasothertypesoftiesmightisolatetheidenticalgridthroughdifferentlinksduetotheirhighMoran’sindex.Theoverlapreducesthenumberofpassivelyisolatedgrids,therebydiminishingtheefficiencyofquarantinemeasuresundertheassumptionthatvariousisolatedgridscanconcurrentlyandindependentlyselecttheircom