参考文献

参考文献

[1]Bernoulli D.Essai d'une nouvelle analyse de la mortalit'e caus'ee par la petite v'erole et des avantages de l'inoculation pour la pr'evenir[J].Histoire de l'Acad.Roy.Sci.(Paris)avec M'em.des Math.et Phys.and M'em,1760:1-45.

[2]Pastor-Satorras R,Vespignani A.Epidemic spreading in scale-free networks[J].Physical Review Letters,2001,86(14):3200.

[3]Keeling M J,Rohani P.Modeling infectious diseases in humans and animals[M].Princeton University Press,2008.

[4]Ferreira S C,Castellano C,Pastor-Satorras R.Epidemic thresholds of the susceptibleinfected-susceptible model on networks:A comparison of numerical and theoretical results[J].Physical Review E,2012,86(4):041125.

[5]Shu P,Wang W,Tang M,et al.Numerical identification of epidemic thresholds for susceptible-infected-recovered model on finite-size networks[J].Chaos,2015,25(6):063104.

[6]Fennell P G,Melnik S,Gleeson J P.Limitations of discrete-time approaches to continuous-time contagion dynamics[J].Physical Review E,2016,94(5):052125.

[7]Wang W,Tang M,Stanley H E,et al.Unification of theoretical approaches for epidemic spreading on complex networks[J].Reports on Progress in Physics,2016,80:036603.

[8]Newman M E.Spread of epidemic disease on networks[J].Physical Review E,2002,66(1):016128.

[9]Wang W,Tang M,Zhang H F,et al.Epidemic spreading on complex networks with general degree and weight distributions[J].Physical Review E,2014,90(4):042803.

[10]Lee H K,Shim P S,Noh J D.Epidemic threshold of the susceptible-infected-susceptible model on complex networks[J].Physical Review E,2013,87(6):062812.

[11]Pastor-Satorras R,Vespignani A.Epidemic dynamics in finite size scale-free networks[J].Physical Review E,2002,65(3):035108.

[12]Yang Z,Zhou T.Epidemic spreading in weighted networks:an edge-based meanfield solution[J].Physical Review E,2012,85(5):056106.

[13]Zhu X,Wang R,Wang Z,et al.Double-edged sword effect of edge overlap on asymmetrically interacting spreading dynamics[J].Physica A:Statistical Mechanics and its Applications,2019,515:617-624.

[14]Moreno Y,G'omez J B,Pacheco A F.Epidemic incidence in correlated complex networks[J].Physical Review E,2003,68(3):035103.

[15]Wang R S,Albert R.Effects of community structure on the dynamics of random threshold networks[J].Physical Review E,2013,87(1):012810.

[16]Barth'elemy M,Barrat A,Pastor-Satorras R,et al.Velocity and hierarchical spread of epidemic outbreaks in scale-free networks[J].Physical Review Letters,2004,92(17):178701.

[17]Xu E H,Wang W,Xu C,et al.Suppressed epidemics in multirelational networks[J].Physical Review E,2015,92(2):022812.

[18]Buono C,Vazquez F,Macr Pi,et al.Slow epidemic extinction in populations with heterogeneous infection rates[J].Physical Review E,2013,88(2):022813.

[19]Boccaletti S,Bianconi G,Criado R,et al.The structure and dynamics of multilayer networks[J].Physics Reports,2014,544(1):1-122.

[20]Kivel M,Arenas A,Barthelemy M,et al.Multilayer networks[J].Journal of Complex Networks,2014,2(3):203-271.

[21]Buono C,Braunstein L A.Immunization strategy for epidemic spreading on multilayer networks[J].EPL(Europhysics Letters),2015,109(2):26001.

[22]Holme P,Saramäk Ji.Temporal networks[J].Physics Reports,2012,519(3):97-125.

[23]Wang L,Li X.Spatial epidemiology of networked metapopulation:An overview[J].Chinese Science Bulletin,2014,59(28):3511-3522

[24]Barth'elemy M.Spatial networks[J].Physics Reports,2011,499(1):1-101.

[25]Zhang Z-K,Liu C,Zhan X-X,et al.Dynamics of information diffusion and its applications on complex networks[J].Physics Reports,2016,651:1-34.

[26]Centola D.An experimental study of homophily in the adoption of health behavior[J].Science,2011,334(6060):1269-1272.

[27]Zhu X,Wang W,Cai S,et al.Dynamics of social contagions with local trend imitation[J].Scientific reports,2018,8(1):1-10.

[28]Zhu X,Wang W,Cai S,et al.Optimal imitation capacity and crossover phenomenon in the dynamics of social contagions[J].Journal of Statistical Mechanics:Theory and Experiment,2018(6):063405.

[29]Funk S,Salath'e M,Jansen V A.Modelling the influence of human behaviour on the spread of infectious diseases:a review[J].Journal of the Royal Society Interface,2010,7(50):1247-1256.

[30]Funk S,Gilad E,Watkins C,et al.The spread of awareness and its impact on epidemic outbreaks[J].Proceedings of the National Academy of Sciences,2009,106(16):6872-6877.

[31]Granell C,G'omez S,Arenas A.Dynamical interplay between awareness and epidemic spreading in multiplex networks[J].Physical Review Letters,2013,111(12):128701.

[32]Granell C,G'omez S,Arenas A.Competing spreading processes on multiplex networks:awareness and epidemics[J].Physical Review E,2014,90(1):012808.

[33]Newman M.E J.Assortative Mixing in Networks[J].Physical Review Letters,2002,89(20):208701.

[34]Pàl Erds,Rény A Ri.On random graphs I[J].Publicationes Mathematicae,1959,6:290-297.

[35]Dame N.Statistical mechanics of complex networks[J].Review of Modern Physics,2002,74(1):xii.

[36]Watts D J,Strogatz S H.Collectivedynamics of‘small-world’networks[J].Nature,1998,393(6684):440-442.

[37]Barabási,Albert-László.Scale-Free Networks:A Decade and Beyond.[J].Science,2009.

[38]Catanzaro M ,Boguñá,Marián,Pastor-Satorras R.Generation of uncorrelated random scale-free networks[J].Physical Review E,2004,71(2 Pt 2):027103.

[39]Wang W,Liu Q H,Liang J,et al.Coevolution spreading in complex networks[J].Physics Reports,2019,820:1-51.

[40]Anderson R M,May R M and Anderson B 1992 Infectious Diseases of Humans:Dynamics and Control vol 28(New York:Wiley)

[41]Moreno Y,Pastor-Satorras R,Vespignani A.Epidemic outbreaks in complex heterogeneous networks[J].The European Physical Journal B-Condensed Matter and Complex Systems,2002,26(4):521-529.

[42]Pastor-Satorras R and Vespignani A 2001 Phys.Rev.Lett,2001,86:3200.

[43]Chu X,Guan J,Zhang Z,et al.Epidemic spreading in weighted scale-free networks with community structure[J].Journal of Statistical Mechanics:Theory and Experiment,2009(7):P07043.

[44]Boguná M,Pastor-Satorras R,Vespignani A.Absence of epidemic threshold in scale-free networks with degree correlations[J].Physical review letters,2003,90(2):028701.

[45]Wang W,Tang M,Yang H,et al.Asymmetrically interacting spreading dynamics on complex layered networks[J].Scientific reports,2014,4:5097.

[46]Saumell-Mendiola A,Serrano M Á,Boguná M.Epidemic spreading on interconnected networks[J].Physical Review E,2012,86(2):026106.

[47]Liu Q H,Wang W,Tang M,et al.Impacts of complex behavioral responses on asymmetric interacting spreading dynamics in multiplex networks[J].Scientific reports,2016,6:25617.

[48]Gómez S,Arenas A,Borge-Holthoefer J,et al.Discrete-time Markov chain approach to contact-based disease spreading in complex networks[J].EPL(Europhysics Letters),2010,89(3):38009.

[49]Van Mieghem P.The N-intertwined SIS epidemic network model[J].Computing,2011,93(2-4):147-169.

[50]Li C,Wang H,Van Mieghem P.Epidemic threshold in directed networks[J].Physical Review E,2013,88(6):062802.

[51]Chung F,Lu L,Vu V.Spectra of random graphs with given expected degrees[J].PNAS,2003,100(11):6313-6318.

[52]Goltsev A V,Dorogovtsev S N,Oliveira J G,et al.Localization and spreading of diseases in complex networks[J].Physical review letters,2012,109(12):128702.

[53]Pastor-Satorras R,Castellano C,Van Mieghem P,et al.Epidemic processes in complex networks[J].Reviews of modern physics,2015,87(3):925.

[54]Newman M.Networks:an Introduction(Oxford:Oxford University Press),2010.

[55]Karrer B,Newman M E J.Message passing approach for general epidemic models[J].Physical Review E,2010,82(1):016101.

[56]Shrestha M,Scarpino S V,Moore C.Message-passing approach for recurrent-state epidemic models on networks[J].Physical Review E,2015,92(2):022821.

[57]Wang W,Liu Q H,Zhong L F,et al.Predicting the epidemic threshold of the susceptible-infected-recovered model[J].Scientific reports,2016,6(1):1-12.

[58]Mata A S,Ferreira S C.Pair quenched mean-field theory for the susceptible-infectedsusceptible model on complex networks[J].EPL (Europhysics Letters),2013,103(4):48003.

[59]Wang W ,Shu P,Zhu Y X,et al.Dynamics of social contagions with limited contact capacity[J].Chaos,2015,25(10):103102.

[60]Zhu X,Yang Q,Tian H ,et al.Contagion of Information on Two-Layered Weighted Complex Network[J].IEEE Access,2019,99:1-1.

[61]Watts,D.J,Dodds,P.S.Infuentials,networks,and public opinion formation.Journal of consumer research,2007,34,441-458.

[62]Castellano C,Fortunato S,Loreto V.Statistical physics of social dynamics.Rev.Mod.Phys,2009,81:591.

[63]Gao L,Wang W,Pan L,et al.Efective information spreading based on local information in correlated networks.Sci.Rep,2016,6.

[64]Christakis N A,Fowler J H.Te spread of obesity in a large social network over 32 years.N.Engl.J.Med,2007,357:370-379.

[65]Barrat A,Barthelemy M.Vespignani A.Dynamical Processes on Complex Networks(Cambridge:Cambridge University Press,2008).

[66]Shu P,Wang W,Tang M,Zhao P,et al.Recovery rate afects the efective epidemic threshold with synchronous updating.Chaos,2016,26,063108.

[67]Porter M A,Gleeson J P.Dynamical Systems on Networks.ar Xiv preprint ar Xiv,2014,1403.7663.

[68]Granovetter M S.Te strength of weak ties.Am.J.Sociol,1973,78,1360-1380.

[69]Watts D J.A simple model of global cascades on random networks.Proc.Natl.Acad.Sci,2002,99,5766-5771.

[70]Gleeson J P,Cahalane D J.Seed size strongly afects cascades on random networks.Phys.Rev.E,2007,75,056103.

[71]Kobayashi T.Trend-driven information cascades on random networks.Phys.Rev.E,2015,92,062823.

[72]Whitney D E.Dynamic theory of cascades on fnite clustered random networks with a threshold rule.Phys.Rev.E,2010,82,066110.

[73]Gleeson J P.Cascades on correlated and modular random networks.Phys.Rev.E,2008,77,046117.

[74]Nematzadeh A.,Ferrara E,Flammini A,et al.Optimal network modularity for information difusion.Phy.Rev.Lett,2014,113,088701.

[75]Lee K M.,Brummitt C D,Goh K I.Treshold cascades with response heterogeneity in multiplex networks.Phys.Rev.E,2014,90,062816.

[76]Takaguchi T,Masuda N,Holme P.Bursty communication patterns facilitate spreading in a threshold-based epidemic dynamics.PloS one.2013,8:e68629.

[77]Dodds P S,Watts D J.Universal behavior in a generalized model of contagion.Phy.Rev.Lett,2004,92:218701.

[78]Zheng M,LüL,Zhao M.Spreading in online social networks:Te role of social reinforcement.Phys.Rev.E,2013,88,012818.

[79]Wang W,Tang M,Zhang H F ,Lai Y C.Dynamics of social contagions with memory of nonredundant information.Phys.Rev.E,2015,92:012820.

[80]Wang W,Tang M,Shu,P,Wang Z.Dynamics of social contagions with heterogeneous adoption thresholds:crossover phenomena in phase transition.New J.Phys,2016,18:013029.

[81]Liu M X.et al.Social contagions on time-varying community networks.Phys.Rev.E,2017,95:052306.

[82]Leibenstein H.Inside the frm:the inefciencies of hierarchy.(Harvard University Press,Cambridge,MA,1987.

[83]Simmel G.Fashion.Am.J.Sociology,1957,62:541-558.

[84]Granovetter M,Soong R.Treshold models of interpersonal efects in consumer demand.J.Econ.Behav.Organ,1986,7:83-99.

[85]Dodds P S,Harris K D,Danforth C M.Limited imitation contagion on random networks:Chaos,universality,and unpredictability.Phys.Rev.Lett,2013,110:158701.

[86]Miller J C,Slim A C,Volz E M.Edge-based compartmental modelling for infectious disease spread.J.R.Soc.Interface,2012,9:890-906.

[87]Miller J C,Volz E M.Incorporating disease and population structure into models of SIR disease in contact networks.PloS One,2013,8:e69162.

[88]Chen W,Schröder M,D'Souza R M.,Sornette,D,Nagler,J.Microtransition cascades to percolation.Phys.Rev.Lett,2014,112:155701.

[89]Watts D J,Dodds P S.Influentials,networks,and public opinion formation J.Consci.Res,200,34:441-58.

[90]Wang W,Tang M,Yang H,et al.Asymmetrically interacting spreading dynamicson complex layered networks Sci.Rep,2014,4:5097.

[91]Qi H K,Liu L D,Meng X Z.Dynamics of a nonautonomous stochastic SIS epidemic model with double epidemic hypothesis Complexity 2017:4861391.

[92]Malik H A M,et al.Robustness of dengue complex network under targeted versus random attack Complexity,2017:2515928.

[93]Chen X L,Wang R J,Tang M,et al.Suppressing epidemic spreading in multiplex networks with social-support New J.Phys,2018:20013007.

[94]Chen X L,Wang W,Cai S M,et al.Optimal resource diffusion for suppressing disease spreading in multiplex networks J.Stat.Mech,2018:053501.

[95]Porter M A,Gleeson J P.Dynamical Systems on Networks:a Tutorial,Frontiers Applied Dynamical Systems:Reviews and Tutorials(Heidelberg:Springer),2016.

[96]Chen X L,Yang C,Zhong L F,et al.Crossover phenomena of percolation transition in evolution networks with hybrid attachment Chaos,2016,26:083114.

[97]Gleeson J P,Cahalane D J.Seed size strongly affects cascades on random networks Phys.Rev.E,2007,75:056103.

[98]Dodds P S,Payne J L.Analysis of a threshold model of social contagion on degreecorrelated networks Phys.Rev.E,2009.79:066115.

[99]Granovetter M.The strength of weak ties Am.J.Sociol,1973,78:1360-1380.

[100]Karsai M,et al.Local cascades induced global contagion:how heterogeneous thresholds,exogenous effects,and unconcerned behaviour govern online adoption spreading Sci.Rep,2016,6:27178.

[101]Gao L,Wang W,Pan L M,,et al.Effective information spreading based on local information in correlated networks Sci.Rep,2016,6:38220.

[102]Liu X Y,Chao L ,Zeng X P.Online social network emergency public event information propagation and nonlinear mathematical modeling Complexity,2017:5857372.

[103]Aral S,Muchnik L,Sundararajan A.Distinguishing influence-based contagion from homophilydriven diffcusion in dynamic networks Proc.Natl Acad.Sci.USA,2009,106:21544-21549.

[104]Christakis N A,Fowler J H.The spread of obesity in a large social network over 32 years New Engl.J.Med.2007:370.

[105]Zheng M,LüL,Zhao M.Spreading in online social networks:the role of social reinforcement Phys.Rev.E,2013,88:012818.

[106]Karampourniotis P D,et al.The impact of heterogeneous thresholds on social contagion with multiple initiators PLoS One,2015,10:e0143020.

[107]Unicomb S,I~niguez G,Karsai M.Threshold driven contagion on weighted networks Sci.Rep.2018,8:3094.

[108]Backlund V P,Saramäki J,Pan R K.Effects of temporal correlations on cascades:threshold models on temporal networks Phys.Rev.E,2014,89:062815.

[109]Wang W,Cai M,Zheng M.Social contagions on correlated multiplex networks Physica A,2017,499:121.

[110]Wang W,Chen X L,Zhong L F.Social contagions with heterogeneous credibility Physica A,2018,503:604.

[111]Leibenstein H,Inside the Firm:the Ineffciencies of Hierarchy(Cambridge,MA:Harvard University Press),1976.

[112]Simmel G.Fashion Am.J.Sociol,1957,62:541-558.

[113]Granovetter M,Soong R.Threshold models of interpersonal effects in consumer demand J.Econ.Behav.Organ.1986,7:83-99.

[114]Dodds P S,Harris K D,Danforth C M.Limited imitation contagion on random networks:chaos,universality,and unpredictability Phys.Rev.Lett,2013,110:158701.

[115]Arthur W B.Inductive reasoning and bounded rationality Am.Econ.Rev.1994,84:406.

[116]Challet D,Marsili M,Zecchina R.Statistical mechanics of systems with heterogeneous agents:minority games Phys.Rev.Lett,2000,84:1824.

[117]Challet D,Marsili M,Zhang Y C.Stylized facts of financial markets and market crashes in minority games Physica A,2001,294:514.

[118]Challet D,Marsili M,Zhang Y C.Minority Games:Interacting Agents in Financial Markets(Oxford:Oxford University Press),2013.

[119]Erdös P,Rényi.On random graphs Publ.Math.1959,6:290-7.

[120]Liu R R,Wang W X,Lai Y C,et al.Cascading dynamics on random networks:crossover in phase transition Phys.Rev.E,2012,85:026110.

[121]Strogatz S,et al.Nonlinear dynamics and chaos:with applications to physics,biology,chemistry,and engineering Comput.Phys.1994,8:532.

[122]Newman M.Networks:An Introduction,Oxford University Press,2010.

[123]Newman M E.Communities,modules and large-scale structure in networks,Nat.Phys,2012,8(1):25-31.

[124]Cai M,Cui Y,Stanley H E.Analysis and evaluation of the entropy indices of a static network structure,Sci.Rep,2017,7(1):9340.

[125]Cai M,Wang W,Cui Y,et al.Multiplex network analysis of employee performance and employee social relationships,Physica A,2018,490:1-12.

[126]Pastor-Satorras R,Vespignani A.Epidemic dynamics and endemic states in complex networks,Phys.Rev.E,2001,63(6):066117.

[127]Wang L,Wu J T.Characterizing the dynamics underlying global spread of epidemics,Nature Commun,2018,9(1):218.

[128]Zheng M,LüL,Zhao M,et al.Spreading in online social networks:The role of social reinforcement,Phys.Rev.E,2013,88(1):012818.

[129]Gómez-Gardeñes J,Soriano-Paños D,Arenas A.Critical regimes driven by recurrent mobility patterns of reaction-diffusion processes in networks,Nat.Phys,2018,14(4):391.

[130]Domenico M D,Granell C,Porter M A,et al.The physics of spreading processes in multilayer networks,Nat.Phys,2016,12(10):901.

[131]Wu T,Chen L,Xian X,et al.Evolution prediction of multi-scale information diffusion dynamics,Knowl.-Based Syst,2016,133:186-198.

[132]BoguñáM,Castellano C,Pastor-Satorras R,Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks,Phys.Rev.Let,2013,111(6):068701.

[133]Wang W,Liu Q H,Zhong L F,et al.Stanley,Predicting the epidemic threshold of the susceptible-infected-recovered model,Sci.Rep,2016,6:24676.

[134]Yang Z,Zhou T.Epidemic spreading in weighted networks:An edge-based meanfield solution,Phys.Rev.E,2012,85(5):056106.

[135]Gang Y,Tao Z,Jie W,et al.W.Bing-Hong,Epidemic spread in weighted scalefree networks,Chin.Phys.Lett.,2005,22(2):510.

[136]Sun Y,Liu C,Zhang C X,et al.Epidemic spreading on weighted complex networks,Phys.Lett.A,2014,378(7):635-640.

[137]Masuda N,Holme P,Predicting and controlling infectious disease epidemics using temporal networks,F1000prime reports 5.

[138]Arruda G F,Rodrigues F A,Moreno Y.Fundamentals of spreading processes in single and multilayer complex networks,ar Xiv preprint ar Xiv:1804.08777.

[139]Wang Z,Moreno Y,Boccaletti S,et al.Vaccination and Epidemics in Networked Populations:An Introduction,2017.

[140]Clusella P,Grassberger P,Pérez-Reche F J,et al.Immunization and targeted destruction of networks using explosive percolation,Phys.Rev.Lett,2016,117(20):208301.

[141]Schneider C M,Mihaljev T,Havlin S,et al.Suppressing epidemics with a limited amount of immunization units,Phys.Rev.E,2011,84(6):61911.

[142]Del Ferraro G,Moreno A,Min B,et al.Ú.Pérez-Ramírez,L.Pérez-Cervera,L.C.Parra,A.Holodny,S.Canals,H.A.Makse,Finding influential nodes for integration in brain networks using optimal percolation theory,Nature Commun,2018,9(1):2274.

[143]Pei S,Morone F,Makse H A,Theories for influencer identification in complex networks,in:Complex Spreading Phenomena in Social Systems,Springer,2018:125-148.

[144]Pei S,Teng X,Shaman J,et al.Efficient collective influence maximization in cascading processes with first-order transitions,Sci.Rep,2017,7:45240.

[145]Chen D,LüL,Shang M S,et al.Identifying influential nodes in complex networks,Physica A,2012,391(4):1777-1787.

[146]Wu T,Xian X,Zhong L,et al.Stanley,Power iteration ranking via hybrid diffusion for vital nodes identification,Physica A,2018,506:802-815.

[147]Z.Wang,Bauch C T,Bhattacharyya S,et al.Statistical physics of vaccination,Phys.Rep,2016,664:1-113.

[148]Pei S,Makse H A.Spreading dynamics in complex networks,J.Stat.Mech.Theory Exp,2013,12:12002.

[149]LüL,Chen D,Ren X L,et al.Vital nodes identification in complex networks,Phys.Rep,2016,650:1-63.

[150]LüL,Zhou T,Zhang Q M,et al.The h-index of a network node and its relation to degree and coreness,Nature Commun,2016,7:10168.

[151]Zhong L F,Liu Q H,Wang W,et al.Comprehensive influence of local and global characteristics on identifying the influential nodes,Physica A.

[152]Zeng A,Zhang C J.Ranking spreaders by decomposing complex networks,Phys.Lett.A,2013,377(14):1031-1035.

[153]Wu T,Chen L,Zhong L,et al.Enhanced collective influence:A paradigm to optimize network disruption,Physica A,2017,472:43-52.

[154]Morone F,Makse H A,Influence maximization in complex networks through optimal percolation,Nature,2015,524(7563):65.

[155]Hu Y,Ji S,Jin Y,et al.Local structure can identify and quantify influential global spreaders in large scale social networks,Proc.Nat.Acad.Sci,2018:201710547.

[156]Yuan X,Dai Y,Stanley H E,et al.k-core percolation on complex networks:Comparing random,localized,and targeted attacks,Phys.Rev.E,2016,93(6):062302.

[157]Shao S,Huang X,Stanley H E,et al.Percolation of localized attack on complex networks,New J.Phys,2015,17(2):023049.

[158]Leskovec J,Adamic L A,Huberman B A.The dynamics of viral marketing,ACM Trans.Web,2007,1:5.

[159]Viswanath B,Mislove A,Cha M,et al.On the evolution of user interaction in Facebook,in:Proceedings of the 2nd ACM Workshop on Online Social Networks,ACM,2009:37-42.

[160]Leskovec J,Mcauley J J,Learning to discover social circles in ego networks,in:Advances in Neural Information Processing Systems,2012:539-547.

[161]Soffer S N,Vazquez A.Network clustering coefficient without degree-correlation biases,Phys.Rev.E,2005,71(5):057101.

[162]Newman M E.Random graphs with clustering,Phys.Rev.Lett,2009,103(5):058701.

[163]Britton T,Deijfen M,Lagerås A N,et al.Epidemics on random graphs with tunable clustering,J.Appl.Probab,2008,45(3):743-756.

[164]Fortunato S.Community detection in graphs,Phys.Rep,2010,486(3-5):75-174.

[165]Lokhov A Y,Mézard M,Ohta H,et al.Inferring the origin of an epidemic with a dynamic message-passing algorithm,Phys.Rev.E,2014,90(1):012801.

[166]Karrer B,Newman M E,ZdeborováL.Percolation on sparse networks,Phys.Rev.Lett,2014,113(20):208702.

[167]Newman M E,Forrest S,Balthrop J,Email networks and the spread of computer viruses,Phys.Rev.E,2002,66(3):035101.

[168]Karsai M,Iñiguez G,Kaski K,et al.Complex contagion process in spreading of online innovation,J.R.Soc.Interface,2014,11(101):20140694.

[169]Wang W,Stanley H E,Braunstein L A.Effects of time-delays in the dynamics of social contagions,New J.Phys,2018,20(1):013034.

[170]Vosoughi S,Roy D,Aral S,The spread of true and false news online,Science,2018,359(6380):1146-1151.

[171]Nematzadeh A,Ferrara E,Flammini A,et al.Optimal network modularity for information diffusion,Phys.Rev.Lett,2014,113(8):088701.

[172]Noël P A,Davoudi B,Brunham R C,et al.Time evolution of epidemic disease on finite and infinite networks,Phys.Rev.E,2009,79(2):026101.

[173]Parshani R,Carmi S,Havlin S.Epidemic threshold for the susceptible-infectioussusceptible model on random networks,Phys.Rev.Lett,2010,104(25):258701.

[174]Pérez-Reche F J,Ludlam J J,Taraskin S N et al.Synergy in spreading processes:from exploitative to explorative foraging strategies,Phys.Rev.Lett,2011,106(21):218701.

[175]Porter M A,Gleeson J P.Dynamical systems on networks.ar Xiv preprint ar Xiv:1403.7663.

[176]Payne J L,Dodds P S,Eppstein M J.Information cascades on degree-correlated random networks,Phys.Rev.E,2009:026125.

[177]Barabasi A L.The origin of bursts and heavy tails in human dynamics,Nature,2005,435(7039):207.

[178]Brockmann D,Hufnagel L,Geisel T.The scaling laws of human travel,Nature,2006,439(7075):462.(https://www.daowen.com)

[179]Barabási A L.Bursts:The Hidden Patterns Behind Everything We Do,From Your EMail to Bloody Crusades,Penguin,2010.

[180]Vazquez A,Racz B,Lukacs A,et al.Impact of non-Poissonian activity patterns on spreading processes,Phys.Rev.Lett,2007,98(15):158702.

[181]Ni S,Weng W.Impact of travel patterns on epidemic dynamics in heterogeneous spatial metapopulation networks,Phys.Rev.E,2009,79(1):016111.

[182]Min B,Goh K I,Vazquez A.Spreading dynamics following bursty human activity patterns,Phys.Rev.E,2011,83(3):036102.

[183]Yang Z,Cui A X,Zhou T,Impact of heterogeneous human activities on epidemic spreading,Physica A,2011,390(23-24):4543-4548.

[184]Gao L,Wang W,Shu P,et al.Promoting information spreading by using contact memory,Europhys.Lett,2017,118(1):18001.

[185]Gao L,Li R,Shu P,et al.Effects of individual popularity on information spreading in complex networks,Physica A,2018,3489:2-39.

[186]Wang Z,Zhou D Y.Group percolation in interdependent networks,Phys.Rev.E,2018,97(3):032306.

[187]Wang W,Wang Z X,Cai S M.Critical phenomena of information spreading dynamics on networks with cliques,Phys.Rev.E,2018,98(5):052312.

[188]Newman M E,Strogatz S H,Watts D J.Random graphs with arbitrary degree distributions and their applications,Phys.Rev.E,2001,64(2):026118.

[189]Newman M E.Threshold effects for two pathogens spreading on a network,Phys.Rev.Lett,2005,95(10):108701.

[190]Shu P,Wang W,Tang M,et al.Recovery rate affects the effective epidemic threshold with synchronous updating,Chaos,2016,26(2):063108.

[191]Liu R R,Wang W X,Lai Y C,et al.Cascading dynamics on random networks:Crossover in phase transition,Phys.Rev.E,2012,85(2):026110.

[192]Shu P,Liu Q H,Wang S,et al.Social contagions on interconnected networks of heterogeneous populations,Chaos,2018,28(11):113114.

[193]Wang L,Wang Z,Zhang Y,et al.How human location-specific contact patterns impact spatial transmission between populations?Sci.Rep,2013,3:1468.

[194]Gross T,DLima C J D,Blasius B,Epidemic dynamics on an adaptive network,Phys.Rev.Lett,2006,96(20):208701.

[195]Li R,Wang W,Di Z/Effects of human dynamics on epidemic spreading in cte divoire,Physica A,2017,467:30-40.

[196]Li R,Richmond P,Roehner B M,Effect of population density on epidemics,Physica A,2018,510:713-724.

[197]Chen X L,Wang R J,Yang J C,et al.Hybrid resource allocation and its impact on the dynamics of disease spreading,Physica A,2019,513:156-165.

[198]Zanette D H.Dynamics of rumor propagation on small-world networks,Phys.Rev.E,2002,65(4):041908.

[199]Liu Z,Lai Y C,Ye N,Propagation and immunization of infection on general networks with both homogeneous and heterogeneous components,Phys.Rev.E,2003,67(3):031911.

[200]Noh J D,Rieger H,Random walks on complex networks,Phys.Rev.Lett,2004,92(11):118701.

[201]Zhou J,Liu Z,Li B,Influence of network structure on rumor propagation,Phys.Lett.A,2007,368(6):458-463.

[202]Funk S,Gilad E,Jansen V,Endemic disease,awareness,and local behavioural response,J.Theoret.Biol,2010,264(2):501-509.

[203]Funk S,Jansen V A.Interacting epidemics on overlay networks,Phys.Rev.E Stat.Nonlinear Soft Matter Phys,2010,81(2):036118.

[204]Sahneh F D,Chowdhury F N,Scoglio C M.On the existence of a threshold for preventive behavioral responses to suppress epidemic spreading,Sci.Rep,2012,2:632.

[205]Ruan Z,Tang M,Liu Z.Epidemic spreading with information-driven vaccination,Phys.Rev.E,2012,86(3):036117.

[206]Domenico M D,Solribalta A,Cozzo E,et al.Mathematical formulation of multilayer networks,Phys.Rev.X,2014,3(4):4192-4195.

[207]Gómez S,Díazguilera A,Gómezgardees J,et al.Diffusion dynamics on multiplex networks,Phys.Rev.Lett,2013,110(2):028701.

[208]De D M,Nicosia V,Arenas A,et al.Structural reducibility of multilayer networks,Nature Commun,2015,6:6864.

[209]Kim J Y,Goh K I.Coevolution and correlated multiplexity in multiplex networks,Phys.Rev.Lett,2013,111(5):058702.

[210]Li R,Wang W,Shu P,et al.Review of threshold theoretical analysis about epidemic spreading dynamics on complex networks,Complex Syst.Complex.Sci,2016,13(1):1-39.

[211]Wang G J,Xie C.Tail dependence structure of the foreign exchange market:A network view,Expert Syst.Appl,2015,46(C):164-179.

[212]Wang G J,Xie C,Stanley H E.Correlation structure and evolution of world stock markets:Evidence from pearson and partial correlation-basednetworks,Comput.Econm2018,51(3):607-635.

[213]Wang G J,Xie C.Correlation structure and dynamics of international real estate securities markets:A network perspective,Physica A,2015,424:176-193.

[214]Li R,Dong L,Zhang J,et al.Stanley,Simple spatial scaling rules behind complex cities,Nature Commun,2017,8:1841.

[215]Wu Q,Fu X,Small M,et al.The impact of awareness on epidemic spreading in networks,Chaos,2012,22(1):013101.

[216]Zhang H F,Xie J R,Tang M,et al.Suppression of epidemic spreading in complex networks by local information based behavioral responses,Chaos,2014,24(4):043106.

[217]Cellai D,López E,Zhou J,et al.Percolation in multiplex networks with overlap,Phys.Rev.E,2013,88(5):052811.

[218]Erdös P,Rényi A.On random graphs i,Publ.Math.Debrecen,1959,6:290-297.

[219]Lomi A,Pattison P E.Manufacturing Relations[J].Organization ence,2006.

[220]Kyu-Min L,Jae-Suk Y,Gunn K,et al.Impact of the Topology of Global Macroeconomic Network on the Spreading of Economic Crises[J].Plos One,2011,6(3):e18443.

[221]Du,Wen-Bo,Zhu,et al.Analysis of the Chinese Airline Network as multi-layer networks[J].Transportation Research Part E Logistics&Transportation Review,2016.

[222]Gao J,Buldyrev S V,Stanley H E,et al.Networks formed from interdependent networks[J].Nature Physics,2012,8(1):40-48.

[223]Kurant M,Thiran P.Layered Complex Networks[J].Physical Review Letters,2006,96(13):138701.

[224]Kenett D Y.Perc M and Boccaletti S.Networks of networks-An introduction[J].Chaos Solitons & Fractals the Interdiplinary Journal of Nonlinear ence &Nonequilibrium&Complex Phenomena,2015,80:1-6.

[225]Dickison M,Havlin S,Stanley H E.Epidemics on Interconnected Networks[J].Physical Review E Statistical Nonlinear& Soft Matter Physics,2012,85(2):1380-1404.

[226]Wang Z,Andrews M A,Wu Z X,et al.Coupled disease-behavior dynamics on complex networks:A review[J].Physics of life reviews,2015,15:1-29.

[227]Zhang H F,Xie J R,Chen H S,et al.Impact of asymptomatic infection on coupled disease-behavior dynamics in complex networks[J].EPL (Europhysics Letters),2016,114(3):38004.

[228]Kan J Q,Zhang H F.Effects of awareness diffusion and self-initiated awareness behavior on epidemic spreading-an approach based on multiplex networks[J].Communications in Nonlinear Science and Numerical Simulation,2017,44:193-203.

[229]Buldyrev S V,Parshani R,Paul G,et al.Catastrophic cascade of failures in interdependent networks[J].Nature,2010,464(7291):1025-1028.

[230]Albert R,Jeong H,Barabási A L.Error and attack tolerance of complex networks[J].nature,2000,406(6794):378-382.

[231]Zhang X,Boccaletti S,Guan S,et al.Explosive synchronization in adaptive and multilayer networks[J].Physical review letters,2015,114(3):038701.

[232]Boccaletti S,Almendral J A,Guan S,et al.Explosive transitions in complex networks'structure and dynamics:Percolation and synchronization[J].Physics Reports,2016,660:1-94.

[233]Wang Z,Szolnoki A,Perc M.Optimal interdependence between networks for the evolution of cooperation[J].Scientific reports,2013,3:2470.

[234]Amaral M A,Wardil L,Perc M,et al.Evolutionary mixed games in structured populations:Cooperation and the benefits of heterogeneity[J].Physical Review E,2016,93(4):042304.

[235]Wang Z,Wang L,Szolnoki A,et al.Evolutionary games on multilayer networks:a colloquium[J].The European physical journal B,2015,88(5):1-15.

[236]NEWMAN M.Networks:an introduction.[Sl]:Oxford University Press,2010[J].Citado nas.

[237]Wang Z,Szolnoki A,Perc M.Evolution of public cooperation on interdependent networks:The impact of biased utility functions[J].EPL(Europhysics Letters),2012,97(4):48001.

[238]Wang Z,Szolnoki A,Perc M.Interdependent network reciprocity in evolutionary games[J].Scientific reports,2013,3:1183.

[239]Sanz J,Xia C Y,Meloni S,et al.Dynamics of interacting diseases[J].Physical Review X,2014,4(4):041005.

[240]Wang Z,Szolnoki A,Perc M.Self-organization towards optimally interdependent networks by means of coevolution[J].New Journal of Physics,2014,16(3):033041.

[241]Gleeson J P,O'Sullivan K P,Baños R A,et al.Effects of network structure,competition and memory time on social spreading phenomena[J].Physical Review X,2016,6(2):021019.

[242]de Arruda G F,Cozzo E,Peixoto T P,et al.Disease localization in multilayer networks[J].Physical Review X,2017,7(1):011014.

[243]Wang Z,Wang L,Perc M.Degree mixing in multilayer networks impedes the evolution of cooperation[J].Physical Review E,2014,89(5):052813.

[244]Tejedor A,Longjas A,Foufoula-Georgiou E,et al.Diffusion dynamics and optimal coupling in multiplex networks with directed layers[J].Physical Review X,2018,8(3):031071.

[245]Centola D.The spread of behavior in an online social network experiment[J].science,2010,329(5996):1194-1197.

[246]Porter M A,Gleeson J P.Examples of dynamical systems[M]//Dynamical Systems on Networks.Springer,Cham,2016:5-27.

[247]Centola D.How behavior spreads:The science of complex contagions[M].Princeton University Press,2018.

[248]Zhang H F,Shu P P,Wang Z,et al.Preferential imitation can invalidate targeted subsidy policies on seasonal-influenza diseases[J].Applied Mathematics and Computation,2017,294:332-342.

[249]Yagˇan O,Gligor V.Analysis of complex contagions in random multiplex networks[J].Physical Review E,2012,86(3):036103.

[250]Lee K M,Kim J Y,Cho W,et al.Correlated multiplexity and connectivity of multiplex random networks[J].New Journal of Physics,2012,14(3):033027.

[251]Brummitt C D,Lee K M,Goh K I.Multiplexity-facilitated cascades in networks[J].Physical Review E,2012,85(4):045102.

[252]Lee K M,Brummitt C D,Goh K I.Threshold cascades with response heterogeneity in multiplex networks[J].Physical Review E,2014,90(6):062816.

[253]Chen L J,Chen X L,Cai M,et al.Complex contagions with social reinforcement from different layers and neighbors[J].Physica A:Statistical Mechanics and its Applications,2018,503:516-525.

[254]Gonzalez M C,Hidalgo C A,Barabasi A L.Understanding individual human mobility patterns[J].nature,2008,453(7196):779-782.

[255]Perc M.Does strong heterogeneity promote cooperation by group interactions[J].New Journal of Physics,2011,13(12):123027.

[256]Yang H,Tang M,Gross T.Large epidemic thresholds emerge in heterogeneous networks of heterogeneous nodes[J].Scientific reports,2015,5:13122.

[257]Chen X,Perc M.Optimal distribution of incentives for public cooperation in heterogeneous interaction environments[J].Frontiers in Behavioral Neuroscience,2014,8:248.

[258]Wang Q,Wang H,Zhang Z,et al.Heterogeneous investments promote cooperation in evolutionary public goods games[J].Physica A:Statistical Mechanics and its Applications,2018,502:570-575.

[259]Karampourniotis P D,Szymanski B K,Korniss G.Influence Maximization for Fixed Heterogeneous Thresholds[J].Scientific reports,2019,9(1):1-12.

[260]Yuan X,Hu Y,Stanley H E,et al.Eradicating catastrophic collapse in interdependent networks via reinforced nodes[J].Proceedings of the National Academy of Sciences,2017,114(13):3311-3315.

[261]Suo Q,J.Guo L,Shen A Z.“Information spreading dynamics in hypernetworks,”Phys.A,Stat.Mech.Appl,2018,495:475-487.

[262]Lei K,Zhang K,Xu K.“Understanding sina weibo online social network:A community approach,”in Proc.IEEE Global Commun.Conf.(GLOBECOM),Dec.2013:3114-3119.

[263]Mazman S G,Usluel Y K.“Modeling educational usage of Facebook,”Comput.Educ,2010,55(2):444-453.

[264]Zhao J,Wu J,Xu K.“Weak ties:Subtle role of information diffusion in online social networks,”Phys.Rev.E,Stat.Phys.Plasmas Fluids Relat.Interdiscip.Top.,2010,82(1):016105.

[265]Kim Y,Srivastava J.“Impact of social inflfluence in e-commerce decision making,”in Proc.9th Int.Conf.Electron.Commerce,2007:293-302.

[266]Berger N,Borgs C,Chayes J T,et al.“On the spread of viruses on the Internet,”in Proc.16th Annu.ACM-SIAM Symp.Discrete Algorithms,2005:301-310.

[267]Moreno Y,Nekovee M,Pacheco A F.“Dynamics of rumor spreading in complex networks,”Phys.Rev.E,Stat.Phys.Plasmas Fluids Relat.Interdiscip.Top.,2004,69(6):066130.

[268]Zhang H F,Shu P P,Wang Z,et al.“Preferential imitation can invalidate targeted subsidy policies on seasonalinflfluenza diseases,”Appl.Math.Comput.,2017,294:332-342.

[269]BogunáM,Pastor-Satorras R.“Epidemic spreading in correlated complex networks,”Phys.Rev.Lett.,2002,66(4):047104.

[270]Liu Z,Hu B.“Epidemic spreading in community networks,”EPL(Europhys.Lett.),2005,72(2):315.

[271]Yang Z,Zhou T.“Epidemic spreading in weighted networks:An edgebased mean-fifield solution,”Phys.Rev.E,Stat.Phys.Plasmas Fluids Relat.Interdiscip.Top,2012,85(5):056106.

[272]Zhang H F,Xu F,Bao Z K,et al.“Reconstructing of networks with binary-state dynamics via generalized statistical inference,”IEEE Trans.Circuits Syst.I,Reg.Papers,2018,66(4):1608-1619.

[273]Borge-Holthoefer J,Moreno Y.“Absence of inflfluential spreaders in rumor dynamics,”Phys.Rev.E,Stat.Phys.Plasmas Fluids Relat.Interdiscip.Top,2012,85(2):026116.

[274]Comin C H,Fontoura Costa L.“Identifying the starting point of a spreading process in complex networks,”Phys.Rev.E,Stat.Phys.Plasmas Fluids Relat.Interdiscip.Top,2011,84(11):056105.

[275]Barrat A,Barthélemy M,Vespignani A,“Modeling the evolution of weighted networks,”Phys.Rev.E,Stat.Phys.Plasmas Fluids Relat.Interdiscip.Top,2004,70(6):066149.

[276]Zhu Y X,Wang W,Tang M,et al.“Social contagions on weighted networks,”Phys.Rev.E,Stat.Phys.Plasmas Fluids Relat.Interdiscip.Top,2017,96(1):012306.

[277]Centola D,Eguíluz V M,Macy M W.“Cascade dynamics of complex propagation,”Phys.A,Stat.Mech.Appl,2007,374(1):449-456.

[278]Medo M,Zhang Y C,Zhou T.“Adaptive model for recommendation of news,”EPL(Europhys.Lett.),2009,88(3):38005.

[279]Krapivsky P L,Redner S,Volovik D.“Reinforcement-driven spread of innovations and fads,”EPL(Europhys.Lett.),2011,12:P12003.

[280]Barabási A L,Bonabeau E,“Scale-free networks,”Sci.Amer,2003,288(5):60-69.

[281]Miller J C,Volz E M.“Incorporating disease and population structure into models of sir disease in contact networks,”PLoS ONE,2013,8(8):e69162.

[282]Shu P,Wang W,Tang M,et al.“Numerical identifification of epidemic thresholds for susceptible-infected-recovered model on fifinitesize networks,”Chaos,Interdiscipl.J.Nonlinear Sci,2015,25(6):063104.

[283]Peyton Young H.“The dynamics of social innovation,”Proceedings of the National Academy of Sciences,2011,108(4):21285-21291.

[284]Damon Centola.“An Experimental Study of Homophily in the Adoption of Health Behavior,”Science,2011,334(6060):1269-1272.

[285]Banerjee A,Chandrasekhar A G,Duflo E,et al.“The Diffusion of Microfinance,”Science,2013,341(6144):1236498.

[286]Dong Yuxiao,Chawla,Nitesh V,et al.“User modeling on demographic attributes in big mobile social networks,”ACM Transactions on Information Systems(TOIS),2017,35(4):35.

[287]Mahmoudi,Amin,Yaakub,et al.“The Relationship between Online Social Network Ties and User Attributes,”ACM Transactions on Knowledge Discovery from Data(TKDD),2019,13(3):26.

[288]Mahmoudi,Amin,Yaakub,et al.“Continuous-Time User Modeling in Presence of Badges:A Probabilistic Approach,”ACM Transactions on Knowledge Discovery from Data(TKDD),2018,12(3):37.

[289]Wang W,Stanley H E,Braunstein L A.“Effects of time-delays in the dynamics of social contagions”New Journal of Physics,2018,20(1):013034.

[290]Bellingeri M,Bevacqua,D,Scotognella,F,et al.“The heterogeneity in link weights may decrease the robustness of real-world complex weighted networks,”Scientific reports,2019,9(1):1-13.

[291]Liu X,Yu X,Gao Z,et al.“Comparing community-based information adoption and diffusion across different microblogging sites,”Proceedings of the 27th ACM Conference on Hypertext and Social Media,2016:103-112.

[292]Zhu P,Dai X,Li X,et al.“Community detection in temporal networks via a spreading process,”EPL(Europhysics Letters),2019,125(4):48001.

[293]Zhu P,Wang X,Zhi Q,et al.“Analysis of epidemic spreading process in multicommunities,”Chaos,Solitons&Fractals,2018,109:231-237.

[294]Haerter,Jan O,Jamtveit,e al.“Communication dynamics in finite capacity social networks,”Physical Review Letters,2012,109(16):168701.

[295]Cui Peng-Bi,Wang Wei,Cai,Shi-Min,et al.“Close and ordinary social contacts:How important are they in promoting large-scale contagion,”Physical Review E,2018,98(5):052311.

[296]Miritello,Giovanna,Lara,et al.“Time allocation in social networks:correlation between social structure and human communication dynamics,”Temporal networks,2013:175-190.

[297]Golder,Scott A,Wilkinson,et al.“Rhythms of social interaction:Messaging within a massive online network,”Communities and technologies,2007:41-66.

[298]Nicola P,Brun G,Romualdo P,et al“Activity driven modeling of time varying networks,”Scientific reports,2012,2:469.

[299]Márton K and Nicola P and Alessandro V.“Time varying networks and the weakness of strong ties,”Scientific reports,2014,4:4001.

[300]Boccaletti S,Bianconi G,Criado R,et al.“The structure and dynamics of multilayermultilayer networks,”Physics Reports,2014,544(1):1-122.

[301]Kivel M,Arenas A,Barthelemy M,et al.“Multilayer Multilayer networks,”Journal of complex networks,2014,2(3):203-271.

[302]Wang Z,Wang L,Szolnoki A,et al.“Evolutionary games on multilayermultilayer networks:a colloquium,”The European physical journal B,2015,88(5):124.

[303]Zhu X,Tian H and Chen X,et al.“Heterogeneous behavioral adoption in multiplex networks,”New Journal of Physics,2018,20(12):125002.

[304]Zhu P,Zhi Q,Guo Y,et al.“Analysis of epidemic spreading process in adaptive networks,”IEEETransactions on Circuits and Systems II:Express Briefs,2018,66(7):1252-1256.

[305]Pan L,Wang W,Cai S,et al.“Optimal interlayer structure for promoting spreading of the susceptible-infected susceptible model in two-layer networks,”Physical Review E,2018,100(2):022316.

[306]Zhu X,Ma J,Su X,et al.“Information Spreading on Weighted Multiplex Social Network,”Complexity,2019.

[307]Zhu P,Song X,Liu L,et al.“Stochastic analysis of multiplex Boolean networks for understanding epidemic propagation,”IEEE access,2018,6:35292-35304.

[308]Zhu P,Wang X,Li S,et al.“Investigation of epidemic spreading process on multiplex networks by incorporating fatal properties,”Applied Mathematics and Computation,2019,359:512-524.

[309]Shu P,Gao L,Zhao P,et al.H Eugene.“Social contagions on interdependent lattice networks,”Scientific reports,2017,7:44669.

[310]Wang X,Li W H,Liu L Z,et al.“Promoting information diffusion through interlayer recovery processes in multiplex networks,”Physical Review E,2017.96(3):032304.

[311]Krapivsky P L and Redner S,Volovik D.“Reinforcementdriven spread of innovations and fads,”EPL(Europhysics Letters),2011,12:12003.

[312]Miller J C,Volz E M.“Incorporating disease and population structure into models of sir disease in contact networks.”PloS One,2013,8(8):e69162.

[313]Shu P,Wang W,Tang M,et al.“Numerical identification of epidemic thresholds for susceptible-infected recovered model on finite-size networks,”Chaos: An Interdisciplinary Journal of Nonlinear Science,2015,25(6):063104.

[314]Roger G,Leon D,Albert D G,et al.“Self-similar community structure in a network of human interactions,”Physical review E,2003,68(6):065103.

[315]Parshani R,Buldyrev S V,Havlin S.Interdependent networks:reducing the coupling strength leads to a change from a first to second order percolation transition,Phys.Rev.Lett,2010,105(4):048701.

[316]Rinaldi S M,Peerenboom J P,T.K.Kelly T,Identifying,understanding,and analyzing critical infrastructure interdependencies,IEEE Control Syst.Mag,2001,21(6):11-25.

[317]Yagan O,Qian D,Zhang J,et al.Optimal allocation of interconnecting links in cyber-physical systems:interdependence,cascading failures,and robustness,IEEE Trans.Parallel Distrib,2012,23(9):1708-1720.

[318]Dickison M,Havlin S,Stanley H E.Epidemics on interconnected networks,Phys.Rev.E,2012,85(6):066109.

[319]Valdez L,Rêgo H A,Stanley H,et al.The role of bridge nodes between layers on epidemic spreading,New J.Phys,2018,20(12):125003.

[320]Liu M,Li D,Qin P,et al.Epidemics in interconnected small-world networks,PLoS One,2015,10(3):e0120701.

[321]Zhao D,Wang L,Li S,et al.Immunization of epidemics in multiplex networks,PLoS One,2014,9(11):e112018.

[322]Wang Z,Zhao D W,Wang L,et al,Immunity of multiplex networks via acquaintance vaccination,Europhys.Lett,2015,112(4):48002.

[323]Wang W,Liu Q H,Cai S M,et al.Braunstein,H.E.Stanley,Suppressing disease spreading by using information diffusion on multiplex networks,Sci.Rep,2016,6:29259.

[324]Perc M,Jordan J J,Rand D G,et al.Boccaletti,A.Szolnoki,Statistical physics of human cooperation,Phys.Rep,2017,687:1-51.

[325]Zhang X,Bi H,Guan S,J.et al.Model bridging chimera state and explosive synchronization,Phys.Rev.E,2016,94(1):012204.

[326]Dai Y,Zhang J,Wang W.Interconnecting strategy of bridging multilayer networks to maximize synchronizability,Europhys.Lett,2019,125:18003.

[327]Domenico M D,Solé-Ribalta A,Gómez S,et al.Navigability of interconnected networks under random failures,Proc.Natl.Acad.Sci,2014,111(23):8351-8356.

[328]Reis S D,Hu Y,Babino A,et al.Avoiding catastrophic failure in correlated networks of networks,Nat.Phys,2014,10(10):762.

[329]Gao J,Buldyrev S V,Havlin S,et al.Robustness of a network of networks,Phys.Rev.Lett,2011,107(19):195701.

[330]Gao J,Buldyrev S V,Havlin S,et al.Robustness of a network formed by n interdependent networks with a one-to-one correspondence of dependent nodes,Phys.Rev.E,2012,85(6):066134.

[331]Shao S,Huang X,Stanley H E,et al.Robustness of a partially interdependent network formed of clustered networks,Phys.Rev.E,2014,89(3):032812.

[332]Zhou D,Gao J,Stanley H E,et al.Percolation of partially interdependent scalefree networks,Phys.Rev.E,2013,87(5):052812.

[333]Yuan X,Shao S,Stanley H E,et al.How breadth of degree distribution influences network robustness:comparing localized and random attacks,Phys.Rev.E,2015,92(3);032122.

[334]Shao J,Buldyrev S V,Havlin S,et al.Cascade of failures in coupled network systems with multiple support-dependence relations,Phys.Rev.E,2011,83(3):036116.

[335]Castillo-Chavez C,Huang W,Li J.Competitive exclusion in gonorrhea models and other sexually transmitted diseases[J].SIAM Journal on Applied Mathematics,1996,56(2):494-508.

[336]Andreasen V,Lin J,Levin S A.The dynamics of cocirculating influenza strains conferring partial cross-immunity[J].Journal of mathematical biology,1997,35(7):825-842.

[337]Funk S M.Salath E,Jansen V A.JR Soc[J].Interface,2010,7:1247.

[338]Ferguson N,Anderson R,Gupta S.The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens[J].Proceedings of the National Academy of Sciences,1999,96(2):790-794.

[339]Nowak M A,May R M,Phillips R E,et al.Antigenic oscillations and shifting immunodominance in HIV-1 infections[J].Nature,1995,375(6532):606-611.

[340]Ferguson N M,Galvani A P,Bush R M.Ecological and immunological determinants of influenza evolution[J].Nature,2003,422(6930):428-433.

[341]Abu-Raddad L J,Patnaik P,Kublin J G.Dual infection with HIV and malaria fuels the spread of both diseases in sub-Saharan Africa[J].Science,2006,314(5805):1603-1606.

[342]Cai W,Chen L,Ghanbarnejad F,et al.Avalanche outbreaks emerging in cooperative contagions[J].Nature physics,2015,11(11):936-940.

[343]Chen L,Ghanbarnejad F,Cai W,et al.Outbreaks of coinfections:The critical role of cooperativity[J].EPL(Europhysics Letters),2013,104(5):50001.

[344]Grassberger P,Chen L,Ghanbarnejad F,et al.Phase transitions in cooperative coinfections:Simulation results for networks and lattices[J].Physical Review E,2016,93(4):042316.

[345]Chen L,Ghanbarnejad F,Brockmann D.Fundamental properties of cooperative contagion processes[J].New Journal of Physics,2017,19(10):103041.

[346]Cui P B,Colaiori F,Castellano C.Mutually cooperative epidemics on power-law networks[J].Physical Review E,2017,96(2):022301.

[347]Cui P B,Colaiori F,Castellano C.Effect of network clustering on mutually cooperative coinfections[J].Physical Review E,2019,99(2):022301.

[348]Wang Z,Tang M,Cai S,et al.Self-awareness control effect of cooperative epidemics on complex networks[J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2019,29(5):053123.

[349]Mårtensson L,Hensing G.Health literacy-a heterogeneous phenomenon:a literature review[J].Scandinavian journal of caring sciences,2012,26(1):151-160.

[350]Reibel D K,Greeson J M,Brainard G C,et al.Mindfulness-based stress reduction and health-related quality of life in a heterogeneous patient population[J].General hospital psychiatry,2001,23(4):183-192.

[351]Cui A X,Wang W,Tang M,et al.Efficient allocation of heterogeneous response times in information spreading process[J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2014,24(3):033113.

[352]Reibel D K,Greeson J M,Brainard G C,et al.Mindfulness-based stress reduction and health-related quality of life in a heterogeneous patient population[J].General hospital psychiatry,2001,23(4):183-192.

[353]Yang G L,Yang X.Optimal epidemic spreading on complex networks with heterogeneous waiting time distribution[J].Physica A:Statistical Mechanics and its Applications,2016,447:386-391.

[354]Chen N,Zhu X,Chen Y.Information spreading on complex networks with general group distribution[J].Physica A:Statistical Mechanics and its Applications,2019,523:671-676.

[355]Wang R,Chen X,Cai S.Local information based resource allocation model for disease suppressing on complex networks[J].Physica A:Statistical Mechanics and its Applications,2019,533:121968.

[356]Chen X,Liu Q,Wang R,et al.Self-Awareness-Based Resource Allocation Strategy for Containment of Epidemic Spreading[J].Complexity,2020.