The-hidden-geometry-of-complex--network-driven-con

DOI:10.1126/science.1245200,1337(2013);342ScienceDirkBrockmannandDirkHelbingPhenomenaTheHiddenGeometryofComplex,Network-DrivenContagionThiscopyisforyourpersonal,non-commercialuseonly.clickinghere.colleagues,clients,orcustomersby,youcanorderhigh-qualitycopiesforyourIfyouwishtodistributethisarticletoothers here.followingtheguidelinescanbeobtainedbyPermissiontorepublishorrepurposearticlesorportionsofarticles ):December18,2013(thisinformationiscurrentasofThefollowingresourcesrelatedtothisarticleareavailableonlineat:includinghigh-resolutionfigures,canbefoundintheonlineUpdatedinformationandservices,:SupportingOnlineMaterial:canberelatedtothisarticleAlistofselectedadditionalarticlesontheScienceWebsites:cites35articlesThisarticle:citedbyThisarticlehasbeenregisteredtrademarkofAAAS.isaScience2013bytheAmericanAssociationfortheAdvancementofScience;allrightsreserved.ThetitleCopyrightAmericanAssociationfortheAdvancementofScience,1200NewYorkAvenueNW,Washington,DC20005.(printISSN0036-8075;onlineISSN1095-9203)ispublishedweekly,exceptthelastweekinDecember,bytheScienceonDecember18,2013*andDirkHelbing4,5Theglobalspreadofepidemics,rumors,opinions,andinnovationsarecomplex,network-drivendynamicprocesses.Thecombinedmultiscalenatureandintrinsicheterogeneityoftheunderlyingnetworksmakeitdifficulttodevelopanintuitiveunderstandingoftheseprocesses,todistinguishrelevantfromperipheralfactors,topredicttheirtimecourse,andtolocatetheirorigin.However,weshowthatcomplexspatiotemporalpatternscanbereducedtosurprisinglysimple,homogeneouswavepropagationpatterns,ifconventionalgeographicdistanceisreplacedbyaprobabilisticallymotivatedeffectivedistance.Inthecontextofglobal,air-traffic–mediatedepidemics,weshowthateffectivedistancereliablypredictsdiseasearrivaltimes.Evenifepidemiologicalparametersareunknown,themethodcanstilldeliverrelativearrivaltimes.Theapproachcanalsoidentifythespatialoriginofspreadingprocessesandsuccessfullybeappliedtodataoftheworldwide2009H1N1influenzapandemicand2003SARSepidemic.Thegeographicspreadofemergentinfec-tiousdiseasesaffectsthelivesoftensofthousandsorevenmillionsofpeople(1,2).RecentexamplesofemergentdiseasesaretheSARSepidemicof2003,the2009H1N1influenzapandemic,andmostrecentlyanewstrain(H7N9)ofavianinfluenzavirus(3,4).Progressingworld-wideurbanization,combinedwithgrowingcon-nectivityamongmetropolitancenters,hasincreasedtheriskthathighlyvirulentemergentpathogenswillspread(5–8).Thecomplexityofglobalhu-manmobility,particularlyairtraffic(Fig.1A),makesitincreasinglydifficulttodevelopeffec-tivecontainmentandmitigationstrategiesonthetimescaleimposedbythespeedatwhichmod-erndiseasescanspread(9–11).Becausetimely,accurate,andfocusedactioncanpotentiallysavethelivesofmanypeopleandreducethesocio-economicimpactofinfectiousdiseases(12,13),understandingglobaldiseasedynamicshasbe-comeamajor21st-centurychallenge.Unravelingthecoremechanismsthatunderliethesephenome-naandbeingabletodistinguishkeyfactorsfromperipheralonesarerequiredtodevelopquantita-tive,efficient,andpredictivemodelsthatpublichealthauthoritiescanemploytoassesssituationsquickly,makeinformeddecisions,andoptimizevaccinationanddrugdeliveryplans.Afterthein-itialoutbreakofanepidemic,thekeyquestionsareasfollows:(i)Wheredidthenovelpathogenemerge?(ii)Wherearenewcasestobeexpected?(iii)Whenisanepidemicgoingtoarriveatdistantlocations?(iv)Howmanycasesaretobeexpected?Historically,forcaseslikethespreadoftheBlackDeathinEurope,reaction-diffusionmod-elshavebeenquiteusefulinaddressingthesequestions(14,15).Despitetheirhighlevelofabstraction,thesemodelsprovideasolidintuitionandunderstandingofspreadingprocesses.Theirmathematicalsimplicitypermitstheassessmentofkeyproperties,e.g.,spreadingspeed,arrivaltimes,andhowpatterngeometrydependsonsys-temparameters(16).However,becauseoflong-distancetravel,simplereaction-diffusionmodelsareinadequateforthedescriptionoftoday’scom-plex,spatiallyincoherentspreadingpatternsthatgenericallybearnometricregularity,thatdependsensitivelyonmodelparametersandinitialcon-ditions(17–20)(Fig.1,BtoE,andfig.S2).Consequently,scientistshavebeendevelopingpowerful,large-scalecomputationalmodelsandsophisticated,parameter-richepidemicsimulatorsthattackl