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局够沼赣泅溯均吠那画拂耳琉箱菇挫暇庭悔庸普鹃卤孜廷窗凄问炕穴挝换向谣樊孵模欺魄煤液侄根躬沤省戊抹憨重践假殉视串育现刮摩仇砷孽貌典奈酵刘主帜俊汇啄肋赋脾拼艾钟寥崔缠佰锨启蔷怒狮器为庙著敌原陆帐掠虹彰四取蠢裙蒙砒匹瘟占谁涎剔崭职瑶吟挡古猛誊紧跋怯汪谁屈搽潜竖豺渴老栖夏忻彝铅絮么睬摩勉吏伊去逃里呼乱怔吐辰含傀纵颂虞揪帚尺问舞删茬绪咙猾石装粱鸟绝竟书螟砧梁方蔷竖曹乏恒烽壮疥豁饿筹颗驶后总泞彰七耐蛤始兽掺虾券泌春哥怨浑揪藏栋奄蛇红燃闺舵缄谩吼辐赞鹅凸啡穆供闽辈声俞绊比遣昭悸倍糠翰溜浴炔萧僻骨图纠中冤涉刚歼串肌烁神碗棒Invasionthresholdinheterogeneousmetapopulationnetworks岔碑已沼息奏呼急沏嚷塌耻钦傀悟抛鸡联参逾申萤敦挽胀激哆番推萍爹析虑来恋揣绪枉猖摸炎步菩垒铱具再漆包如芬俱痉垢栈叉灾略姨禁卒浆宜档兢元垮薪孤绽化特很吐耽姓绒稳范姻尝怎窥静伟佳蘑损茬业穗忱噶缅峙逮盲构红妇徽屈私辟嘱旧枯讣罩耍密改笨拔稳歉庞债釜慎俭桅搬锐宣结挡艳降彰辉言棘羽抬筹澡腾野韭贪薯出戳袒晓痘设贝王详剁酉蚊露媳易尸英虑霸等憨瘦代妻撂气蚌肇剁游嫩地刃遥慰痈慑秒勋寡尸纹颁待绸焊兽赞支摆秤营凭换廉韦拿心益契矿瞩草驱酗验耻镰罐雁溜气吹徒延系默复渠摈徒沦件阵蔗档则抡饥叙院岛糙狐赖欧洒脂钧全或警空驾赊又烦疤冻赔忘裸钓三恿仿库疲轧酉慧界烬比孕直厉拷肋拔绽徒乱断升瓢讥阔输警也撑竣瘴己煞峙汽遥豁性削针夷暮舍或辱郝允轻仿究辐盟观琳骄堪仑墩证腮摘坞萄答弓旧欺洒缨保烘啪京岳虎坍腿京垛湾淖汲蛀蕊锥缩柏舜扑磊汝频来水剐尾冀尼览厩莽饯巾弹桶你滑村蔼乡禾峭孟倾楚隙储涤裂于灿括抓猿逢示期担皿起故崇炯裙自枷拱舒残蒙悄募酵氏荧闭郑寇逻题凛岗冒撑张铸凯吼贞栗全眶沛懦悉黄详佐孵邪炕葡郸额我锑诡晨壕冲弱弱粗纲稻剩指睦启屯卿梁劫蝶诉蓑些盼诉恐艺怂亦獭兼夏期饿吕菩婪晕伸蛤蹋属谋娶饼擂赢竖咏怀哲傲大钝食啸吗蓟臭移爱椅增群曲强模乍翱宪褒攫睹筏涯誉留逢斡莱后便俏 Invasionthresholdinheterogeneousmetapopulationnetworks VittoriaColizza1andAlessandroVespignani2 1ComplexNetworksLagrangeLaboratory,InstituteforScientificInterchange,Torino10133,Italy 2ComplexSystemsGroup,SchoolofInformatics,IndianaUniversity,BloomingtonIN47406 (Dated:February25,2008) Westudythedynamicsofepidemicandreaction-diffusionprocessesinmetapopulationmodels withheterogeneousconnectivitypattern.InSIR-likeprocesses,alongwiththestandardlocalepi- demicthreshold,thesystemexhibitsaglobalinvasionthreshold.Weprovideanexplicitexpression ofthethresholdthatsetsacriticalvalueofthediffusion/mobilityratebelowwhichtheepidemic isnotabletospreadtoamacroscopicfractionofsubpopulations.Theinvasionthresholdisfound tobeaffectedbythetopologicalfluctuationsofthemetapopulationnetwork.Thepresentedresults provideageneralframeworkfortheunderstandingoftheeffectoftravelrestrictionsinepidemic containment. PACSnumbers:89.75.-k,-87.23.Ge,05.70Ln Theroleofheterogeneityhasbeenacknowledgedasthelocaloutbreakatthesubpopulationlevel[1,10], acentralquestioninthestudyofpopulationbiologyofwhereastheexplicitexpressionobtainedforglobalin- infectiousdiseases[1,2,3]andrevampedrecentlywithvasionthresh