Coevolution spreading in complex networks

Abstract The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic–awareness, and epidemic–resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

[1]  Yamir Moreno,et al.  Contact-based Social Contagion in Multiplex Networks , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Reuven Cohen,et al.  Percolation critical exponents in scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Sergey N. Dorogovtsev,et al.  Critical phenomena in complex networks , 2007, ArXiv.

[4]  Nicola Perra,et al.  Epidemic spreading in modular time-varying networks , 2017, Scientific Reports.

[5]  Tao Zhou,et al.  Onset of cooperation between layered networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Hai-Jun Zhou,et al.  Identifying optimal targets of network attack by belief propagation , 2016, Physical review. E.

[7]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[8]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[9]  Jure Leskovec,et al.  Clash of the Contagions: Cooperation and Competition in Information Diffusion , 2012, 2012 IEEE 12th International Conference on Data Mining.

[10]  Peter Grassberger,et al.  Phase transitions in cooperative coinfections: Simulation results for networks and lattices. , 2015, Physical review. E.

[11]  Ming Tang,et al.  Suppressing epidemic spreading in multiplex networks with social-support , 2017, 1708.02507.

[12]  Dirk Helbing,et al.  Globally networked risks and how to respond , 2013, Nature.

[13]  Y. Moreno,et al.  Epidemic outbreaks in complex heterogeneous networks , 2001, cond-mat/0107267.

[14]  Marián Boguñá,et al.  Clustering in complex networks. I. General formalism. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Douglas Guilbeault,et al.  Complex Contagions: A Decade in Review , 2017, ArXiv.

[16]  Tao Zhou,et al.  Optimal contact process on complex networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  C. Scoglio,et al.  Competitive epidemic spreading over arbitrary multilayer networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Flávio L Pinheiro,et al.  Optimal diversification strategies in the networks of related products and of related research areas , 2017, Nature Communications.

[19]  Gerardo Iñiguez,et al.  Complex contagion process in spreading of online innovation , 2014, Journal of The Royal Society Interface.

[20]  Fan Chung Graham,et al.  The Spectra of Random Graphs with Given Expected Degrees , 2004, Internet Math..

[21]  Cameron Marlow,et al.  A 61-million-person experiment in social influence and political mobilization , 2012, Nature.

[22]  M. Newman,et al.  Interacting Epidemics and Coinfection on Contact Networks , 2013, PloS one.

[23]  Cristopher Moore,et al.  A message-passing approach for recurrent-state epidemic models on networks , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Víctor M Eguíluz,et al.  Epidemic threshold in structured scale-free networks. , 2002, Physical review letters.

[25]  Ming Tang,et al.  Suppression of epidemic spreading in complex networks by local information based behavioral responses , 2014, Chaos.

[26]  Mark S. Granovetter Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[27]  Zhi-Dan Zhao,et al.  Relative clock verifies endogenous bursts of human dynamics , 2012 .

[28]  Lei Gao,et al.  Effective information spreading based on local information in correlated networks , 2016, Scientific Reports.

[29]  Gerardo Iñiguez,et al.  Threshold driven contagion on weighted networks , 2017, Scientific Reports.

[30]  Michael Small,et al.  Impact of asymptomatic infection on coupled disease-behavior dynamics in complex networks , 2016, 1608.04049.

[31]  Bo Hu,et al.  Efficient routing on complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Jian Jiang,et al.  Resource control of epidemic spreading through a multilayer network , 2018, Scientific Reports.

[33]  Barkat-e-Khuda,et al.  Awareness of sexually transmitted disease among women and service providers in rural Bangladesh , 1997, International journal of STD & AIDS.

[34]  Zhi-Dan Zhao,et al.  Emergence of scaling in human-interest dynamics , 2013, Scientific Reports.

[35]  Samuel Alizon,et al.  Epidemic Spread on Weighted Networks , 2013, PLoS Comput. Biol..

[36]  Qian Zhang,et al.  Epidemic spreading on time-varying multiplex networks , 2018, Physical Review. E.

[37]  P. Francis,et al.  Optimal tax/subsidy combinations for the flu season , 2004 .

[38]  J. Kublin,et al.  Dual Infection with HIV and Malaria Fuels the Spread of Both Diseases in Sub-Saharan Africa , 2006, Science.

[39]  Yamir Moreno,et al.  Fundamentals of spreading processes in single and multilayer complex networks , 2018, Physics Reports.

[40]  Didier Sornette,et al.  Early Warning Signals of Financial Crises with Multi-Scale Quantile Regressions of Log-Periodic Power Law Singularities , 2015, PloS one.

[41]  W. O. Kermack,et al.  Contributions to the mathematical theory of epidemics--I. 1927. , 1991, Bulletin of mathematical biology.

[42]  V. Eguíluz,et al.  Highly clustered scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Ming Tang,et al.  Impacts of Opinion Leaders on Social Contagions , 2018, Chaos.

[44]  R. May,et al.  Systemic risk in banking ecosystems , 2011, Nature.

[45]  Xin Jiang,et al.  Two-stage effects of awareness cascade on epidemic spreading in multiplex networks. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[47]  Mason A. Porter,et al.  Multilayer networks , 2013, J. Complex Networks.

[48]  Scott A. Hale,et al.  Rapid rise and decay in petition signing , 2013, EPJ Data Science.

[49]  Steve Gregory,et al.  Efficient local behavioral change strategies to reduce the spread of epidemics in networks , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  James P Gleeson,et al.  Cascades on correlated and modular random networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  Ira B Schwartz,et al.  Fluctuating epidemics on adaptive networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  Alessandro Vespignani,et al.  Host Mobility Drives Pathogen Competition in Spatially Structured Populations , 2013, PLoS Comput. Biol..

[53]  R. Pastor-Satorras,et al.  Non-mean-field behavior of the contact process on scale-free networks. , 2005, Physical review letters.

[54]  Haijuan Zang,et al.  The effects of global awareness on the spreading of epidemics in multiplex networks , 2018 .

[55]  Tao Zhou,et al.  Epidemic Spreading in Weighted Networks: An Edge-Based Mean-Field Solution , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[56]  Zhongyuan Ruan,et al.  Epidemic spreading with information-driven vaccination. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[57]  James P. Gleeson,et al.  Competition-induced criticality in a model of meme popularity , 2013, Physical review letters.

[58]  Lubos Buzna,et al.  Decelerated spreading in degree-correlated networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  Hui Gao,et al.  Effective traffic-flow assignment strategy on multilayer networks. , 2019, Physical review. E.

[60]  Wei Chen,et al.  Assessing Percolation Threshold Based on High-Order Non-Backtracking Matrices , 2016, WWW.

[61]  Wei Wang,et al.  Comprehensive routing strategy on multilayer networks , 2017, 1701.05307.

[62]  Tobias Preis,et al.  Adaptive nowcasting of influenza outbreaks using Google searches , 2014, Royal Society Open Science.

[63]  Alessandro Vespignani,et al.  Multiscale mobility networks and the spatial spreading of infectious diseases , 2009, Proceedings of the National Academy of Sciences.

[64]  Zhenhua Wang,et al.  Hysteresis loop of nonperiodic outbreaks of recurrent epidemics , 2016, Physical review. E.

[65]  Ginestra Bianconi,et al.  Multilayer Networks , 2018, Oxford Scholarship Online.

[66]  Tao Zhou,et al.  The H-index of a network node and its relation to degree and coreness , 2016, Nature Communications.

[67]  Joel C. Miller,et al.  Mathematics of Epidemics on Networks: From Exact to Approximate Models , 2017 .

[68]  M. Serrano,et al.  Percolation and epidemic thresholds in clustered networks. , 2006, Physical review letters.

[69]  Albert-László Barabási,et al.  Understanding individual human mobility patterns , 2008, Nature.

[70]  Angélica S. Mata,et al.  Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks , 2013, 1305.5153.

[71]  Sudip Samanta,et al.  Awareness programs control infectious disease - Multiple delay induced mathematical model , 2015, Appl. Math. Comput..

[72]  T. Geisel,et al.  The scaling laws of human travel , 2006, Nature.

[73]  P. Van Mieghem,et al.  Virus Spread in Networks , 2009, IEEE/ACM Transactions on Networking.

[74]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.

[75]  Margaret L Brandeau,et al.  Dynamic resource allocation for epidemic control in multiple populations. , 2002, IMA journal of mathematics applied in medicine and biology.

[76]  Julia Poncela-Casasnovas,et al.  Adoption of a High-Impact Innovation in a Homogeneous Population. , 2014, Physical review. X.

[77]  Christos Faloutsos,et al.  Epidemic spreading in real networks: an eigenvalue viewpoint , 2003, 22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings..

[78]  Meng Cai,et al.  Social contagions on correlated multiplex networks , 2017, Physica A: Statistical Mechanics and its Applications.

[79]  M. Newman Clustering and preferential attachment in growing networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[80]  S. Havlin,et al.  Epidemic threshold for the susceptible-infectious-susceptible model on random networks. , 2010, Physical review letters.

[81]  Ming Tang,et al.  Controlling epidemic outbreak based on local dynamic infectiousness on complex networks. , 2018, Chaos.

[82]  James P. Gleeson,et al.  Cascades on clique-based graphs , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[83]  Ling Shi,et al.  Decentralised minimum-time consensus , 2013, Autom..

[84]  Alessandro Vespignani,et al.  Absence of epidemic threshold in scale-free networks with degree correlations. , 2002, Physical review letters.

[85]  Riccardo Zecchina,et al.  Bayesian inference of epidemics on networks via Belief Propagation , 2013, Physical review letters.

[86]  Chuang Liu,et al.  Epidemic Spreading on Weighted Complex Networks , 2013, ArXiv.

[87]  Peter Sheridan Dodds,et al.  Universal behavior in a generalized model of contagion. , 2004, Physical review letters.

[88]  Tao Zhou,et al.  Modeling human dynamics with adaptive interest , 2007, 0711.0741.

[89]  Abhijit Sen,et al.  Effect of time varying transmission rates on the coupled dynamics of epidemic and awareness over a multiplex network. , 2018, Chaos.

[90]  Jaideep Srivastava,et al.  A Generalized Linear Threshold Model for Multiple Cascades , 2010, 2010 IEEE International Conference on Data Mining.

[91]  Francesca Colaiori,et al.  Effect of network clustering on mutually cooperative coinfections. , 2018, Physical review. E.

[92]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[93]  N M Ferguson,et al.  Transmission dynamics and epidemiology of dengue: insights from age-stratified sero-prevalence surveys. , 1999, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[94]  Chris T Bauch,et al.  The impact of media coverage on the transmission dynamics of human influenza , 2011, BMC public health.

[95]  Alexei Vazquez,et al.  Spreading Dynamics Following Bursty Activity Patterns , 2013 .

[96]  Hai-Jun Zhou,et al.  Feedback arcs and node hierarchy in directed networks , 2016, ArXiv.

[97]  Marta C. González,et al.  Modelling the propagation of social response during a disease outbreak , 2015, Journal of The Royal Society Interface.

[98]  Dirk Brockmann,et al.  Fundamental properties of cooperative contagion processes , 2016 .

[99]  Sebastian Funk,et al.  Interacting epidemics on overlay networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[100]  Jaewook Joo,et al.  Pair approximation of the stochastic susceptible-infected-recovered-susceptible epidemic model on the hypercubic lattice. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[101]  Injong Rhee,et al.  On the levy-walk nature of human mobility , 2011, TNET.

[102]  Y. Lai,et al.  Effects of behavioral response and vaccination policy on epidemic spreading - an approach based on evolutionary-game dynamics , 2014, Scientific Reports.

[103]  M E J Newman Assortative mixing in networks. , 2002, Physical review letters.

[104]  Wei Wang,et al.  Emergence of hysteresis loop in social contagions on complex networks , 2017, Scientific Reports.

[105]  N. Ling The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[106]  Luc Berthouze,et al.  Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis , 2014, Journal of mathematical biology.

[107]  Sergey N. Dorogovtsev,et al.  Localization and Spreading of Diseases in Complex Networks , 2012, Physical review letters.

[108]  Bryan T Grenfell,et al.  Multiannual forecasting of seasonal influenza dynamics reveals climatic and evolutionary drivers , 2014, Proceedings of the National Academy of Sciences.

[109]  Hyunggyu Park,et al.  Asymmetrically coupled directed percolation systems. , 2005, Physical review letters.

[110]  G S Zaric,et al.  Resource allocation for epidemic control over short time horizons. , 2001, Mathematical biosciences.

[111]  Yaohui Pan,et al.  The impact of individual heterogeneity on the coupled awareness-epidemic dynamics in multiplex networks. , 2018, Chaos.

[112]  H. J. Herrmann,et al.  Disease-induced resource constraints can trigger explosive epidemics , 2014, Scientific Reports.

[113]  Teruyoshi Kobayashi,et al.  Trend-driven information cascades on random networks , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[114]  Huaiping Zhu,et al.  The Impact of Media on the Control of Infectious Diseases , 2007, Journal of dynamics and differential equations.

[115]  Jesús Gómez-Gardeñes,et al.  Abrupt transitions from reinfections in social contagions , 2015 .

[116]  D. Kendall,et al.  Epidemics and Rumours , 1964, Nature.

[117]  A. F. Pacheco,et al.  Epidemic incidence in correlated complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[118]  Lidia A. Braunstein,et al.  Optimal resource diffusion for suppressing disease spreading in multiplex networks , 2018, 1801.03632.

[119]  R. May,et al.  How Viruses Spread Among Computers and People , 2001, Science.

[120]  D. Earn,et al.  Vaccination and the theory of games. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[121]  Akira Sasaki,et al.  The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model , 2002 .

[122]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[123]  Zhou Tao,et al.  Epidemic Spread in Weighted Scale-Free Networks , 2005 .

[124]  Linbo Long,et al.  Malicious viruses spreading on complex networks with heterogeneous recovery rate , 2018, Physica A: Statistical Mechanics and its Applications.

[125]  C. Gilligan,et al.  Synergy in spreading processes: from exploitative to explorative foraging strategies. , 2011, Physical review letters.

[126]  Maria Deijfen,et al.  Epidemics and vaccination on weighted graphs. , 2011, Mathematical biosciences.

[127]  Dong Liu,et al.  Optimal multi-community network modularity for information diffusion , 2016 .

[128]  Alessandro Vespignani,et al.  The role of the airline transportation network in the prediction and predictability of global epidemics , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[129]  Zhongyuan Ruan,et al.  Kinetics of Social Contagion , 2015, Physical review letters.

[130]  E. Oster,et al.  DETERMINANTS OF TECHNOLOGY ADOPTION: PEER EFFECTS IN MENSTRUAL CUP TAKE-UP , 2012 .

[131]  L. A. Braunstein,et al.  Dynamic vaccination in partially overlapped multiplex network , 2018, Physical review. E.

[132]  James P Gleeson,et al.  Bond percolation on a class of clustered random networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[133]  Xin Jiang,et al.  Epidemic spreading with activity-driven awareness diffusion on multiplex network , 2016, Chaos.

[134]  Ming Tang,et al.  Social contagions with communication channels alternation on multiplex networks , 2017, Physical Review E.

[135]  Zi-Gang Huang,et al.  Predicting tipping points in mutualistic networks through dimension reduction , 2018, Proceedings of the National Academy of Sciences.

[136]  N. Ferguson,et al.  The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[137]  B. Althouse,et al.  Complex dynamics of synergistic coinfections on realistically clustered networks , 2015, Proceedings of the National Academy of Sciences.

[138]  Eleftherios Mylonakis,et al.  Google trends: a web-based tool for real-time surveillance of disease outbreaks. , 2009, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[139]  Wei Chen,et al.  Efficient influence maximization in social networks , 2009, KDD.

[140]  Tiago P. Peixoto,et al.  Disease Localization in Multilayer Networks , 2015, Physical Review. X.

[141]  Christopher A. Gilligan,et al.  Resource Allocation for Epidemic Control in Metapopulations , 2011, PloS one.

[142]  L. Stone,et al.  Seasonal dynamics of recurrent epidemics , 2007, Nature.

[143]  Faryad Darabi Sahneh,et al.  Optimal information dissemination strategy to promote preventive behaviors in multilayer epidemic networks. , 2015, Mathematical biosciences and engineering : MBE.

[144]  Clayton Fink,et al.  Complex contagions and the diffusion of popular Twitter hashtags in Nigeria , 2015, Social Network Analysis and Mining.

[145]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[146]  Lin Wang,et al.  Coupled disease–behavior dynamics on complex networks: A review , 2015, Physics of Life Reviews.

[147]  Jonq Juang,et al.  The impact of vaccine success and awareness on epidemic dynamics , 2016, Chaos.

[148]  R. Dickman,et al.  Nonequilibrium Phase Transitions in Lattice Models , 1999 .

[149]  Marián Boguñá,et al.  Synergistic cumulative contagion in epidemic spreading , 2018 .

[150]  Danna Zhou,et al.  d. , 1934, Microbial pathogenesis.

[151]  M. Ajelli,et al.  Reactive school closure weakens the network of social interactions and reduces the spread of influenza , 2019, Proceedings of the National Academy of Sciences.

[152]  Zhi-Xi Wu,et al.  Effect of vaccination strategies on the dynamic behavior of epidemic spreading and vaccine coverage , 2014, Chaos, Solitons & Fractals.

[153]  Yamir Moreno,et al.  Effects of Network Structure, Competition and Memory Time on Social Spreading Phenomena , 2015, Physical Review. X.

[154]  M. Newman Analysis of weighted networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[155]  Yuan Yan Tang,et al.  On the competition of two conflicting messages , 2018 .

[156]  Junjie Zhou,et al.  Key Leaders in Social Networks , 2015, J. Econ. Theory.

[157]  Jinde Cao,et al.  Impact of media coverage on epidemic spreading in complex networks , 2013, Physica A: Statistical Mechanics and its Applications.

[158]  Riccardo Zecchina,et al.  Containing epidemic outbreaks by message-passing techniques , 2013, ArXiv.

[159]  K B Blyuss,et al.  Mathematical model for the impact of awareness on the dynamics of infectious diseases. , 2017, Mathematical biosciences.

[160]  Alessandro Vespignani,et al.  Efficiency and reliability of epidemic data dissemination in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[161]  K Dietz,et al.  Epidemiologic interference of virus populations , 1979, Journal of mathematical biology.

[162]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[163]  Isabel Valera,et al.  Modeling Adoption and Usage of Competing Products , 2014, 2015 IEEE International Conference on Data Mining.

[164]  Daniel P. Maki,et al.  Mathematical models and applications : with emphasis on the social, life, and management sciences , 1973 .

[165]  Aram Galstyan,et al.  Cascading dynamics in modular networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[166]  Beom Jun Kim,et al.  Role of activity in human dynamics , 2007, EPL (Europhysics Letters).

[167]  Andrea Baronchelli,et al.  Contrasting effects of strong ties on SIR and SIS processes in temporal networks , 2015 .

[168]  Victor M. Preciado,et al.  Optimal Containment of Epidemics in Temporal and Adaptive Networks , 2016, ArXiv.

[169]  Wei Huang,et al.  Epidemic spreading in scale-free networks with community structure , 2007 .

[170]  Trevor Cohen,et al.  Content-driven analysis of an online community for smoking cessation: integration of qualitative techniques, automated text analysis, and affiliation networks. , 2015, American journal of public health.

[171]  Wei Wang,et al.  Unification of theoretical approaches for epidemic spreading on complex networks , 2016, Reports on progress in physics. Physical Society.

[172]  Xavier R. Hoffmann,et al.  Memory-induced complex contagion in epidemic spreading , 2018, New Journal of Physics.

[173]  Lars Backstrom,et al.  Structural diversity in social contagion , 2012, Proceedings of the National Academy of Sciences.

[174]  Mason A. Porter,et al.  A simple generative model of collective online behavior , 2013, Proceedings of the National Academy of Sciences.

[175]  R Pastor-Satorras,et al.  Dynamical and correlation properties of the internet. , 2001, Physical review letters.

[176]  Duncan J Watts,et al.  A simple model of global cascades on random networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[177]  Tao Zhou,et al.  Traffic flow and efficient routing on scale-free networks: A survey , 2006 .

[178]  Ming Tang,et al.  Epidemic spreading on complex networks with general degree and weight distributions , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[179]  Tao Zhou,et al.  Unfolding large-scale online collaborative human dynamics , 2015, Proceedings of the National Academy of Sciences.

[180]  Yegor Yakovlev,et al.  Endemic disease , 1955 .

[181]  Hyunggyu Park,et al.  Finite-size scaling in complex networks. , 2007, Physical review letters.

[182]  Guanrong Chen,et al.  Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[183]  Alessandro Vespignani,et al.  Modeling the Worldwide Spread of Pandemic Influenza: Baseline Case and Containment Interventions , 2007, PLoS medicine.

[184]  Lenka Zdeborová,et al.  Dynamic message-passing equations for models with unidirectional dynamics , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[185]  E. Rogers,et al.  Diffusion of innovations , 1964, Encyclopedia of Sport Management.

[186]  Tao Zhou,et al.  Maximal planar networks with large clustering coefficient and power-law degree distribution. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[187]  Ming Tang,et al.  Dynamics of social contagions with memory of non-redundant information , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[188]  Alessandro Flammini,et al.  Optimal network clustering for information diffusion , 2014, Physical review letters.

[189]  C. Scoglio,et al.  On the existence of a threshold for preventive behavioral responses to suppress epidemic spreading , 2012, Scientific Reports.

[190]  V. Jansen,et al.  Endemic disease, awareness, and local behavioural response. , 2010, Journal of theoretical biology.

[191]  Jiming Liu,et al.  A belief-based model for characterizing the spread of awareness and its impacts on individuals' vaccination decisions , 2014, Journal of The Royal Society Interface.

[192]  T. Philipson Economic Epidemiology and Infectious Diseases , 1999 .

[193]  Zhi-Dan Zhao,et al.  Empirical Analysis on the Human Dynamics of a Large-Scale Short Message Communication System , 2011 .

[194]  Sergio Gómez,et al.  On the dynamical interplay between awareness and epidemic spreading in multiplex networks , 2013, Physical review letters.

[195]  C. Bauch,et al.  Social Factors in Epidemiology , 2013, Science.

[196]  Michael Obersteiner,et al.  Systemic trade risk of critical resources , 2015, Science Advances.

[197]  Yi-Cheng Zhang,et al.  Leaders in Social Networks, the Delicious Case , 2011, PloS one.

[198]  Shweta Bansal,et al.  The impact of past epidemics on future disease dynamics. , 2009, Journal of theoretical biology.

[199]  Ernestina Menasalvas Ruiz,et al.  Combining complex networks and data mining: why and how , 2016, bioRxiv.

[200]  E. Volz SIR dynamics in random networks with heterogeneous connectivity , 2007, Journal of mathematical biology.

[201]  Ming Tang,et al.  Numerical identification of epidemic thresholds for susceptible-infected-recovered model on finite-size networks , 2015, Chaos.

[202]  Jia-Rong Xie,et al.  Interplay between the local information based behavioral responses and the epidemic spreading in complex networks , 2015, Chaos.

[203]  Alexei Vázquez,et al.  Exact results for the Barabási model of human dynamics. , 2005, Physical review letters.

[204]  Christos Faloutsos,et al.  Epidemic thresholds in real networks , 2008, TSEC.

[205]  Duanbing Chen,et al.  The small world yields the most effective information spreading , 2011, ArXiv.

[206]  Arun G. Chandrasekhar,et al.  The Diffusion of Microfinance , 2012, Science.

[207]  Zhi-Hong Guan,et al.  Epidemic spreading on networks with overlapping community structure , 2012 .

[208]  B. Bollobás The evolution of random graphs , 1984 .

[209]  A. Hughes,et al.  Evolutionary change of predicted cytotoxic T cell epitopes of dengue virus. , 2001, Infection, genetics and evolution : journal of molecular epidemiology and evolutionary genetics in infectious diseases.

[210]  Daqing Li,et al.  Epidemic mitigation via awareness propagation in communication networks: the role of time scales , 2017 .

[211]  L. D. Valdez,et al.  Social distancing strategies against disease spreading , 2013, 1308.2009.

[212]  H. Stanley,et al.  Networks formed from interdependent networks , 2011, Nature Physics.

[213]  Joel C. Miller,et al.  Supplementary Text S1 , 2014 .

[214]  W. O. Kermack,et al.  Contributions to the mathematical theory of epidemics—I , 1991, Bulletin of mathematical biology.

[215]  S. Carpenter,et al.  Early Warnings of Regime Shifts: A Whole-Ecosystem Experiment , 2011, Science.

[216]  Agnieszka Czaplicka,et al.  Competition of simple and complex adoption on interdependent networks. , 2016, Physical review. E.

[217]  H. Hinrichsen Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[218]  Jari Saramäki,et al.  Small But Slow World: How Network Topology and Burstiness Slow Down Spreading , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[219]  Virgil D. Gligor,et al.  Analysis of complex contagions in random multiplex networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[220]  Michael Small,et al.  The impact of awareness on epidemic spreading in networks , 2012, Chaos.

[221]  C. Watkins,et al.  The spread of awareness and its impact on epidemic outbreaks , 2009, Proceedings of the National Academy of Sciences.

[222]  Wolfgang Lucht,et al.  Tipping elements in the Earth's climate system , 2008, Proceedings of the National Academy of Sciences.

[223]  Yamir Moreno,et al.  Theory of Rumour Spreading in Complex Social Networks , 2007, ArXiv.

[224]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[225]  Mohammad Shafiqur Rahman,et al.  Media and education play a tremendous role in mounting AIDS awareness among married couples in Bangladesh , 2007, AIDS research and therapy.

[226]  Duanbing Chen,et al.  Vital nodes identification in complex networks , 2016, ArXiv.

[227]  Ming Tang,et al.  Explosive spreading on complex networks: the role of synergy , 2016, Physical review. E.

[228]  Hai-Feng Zhang,et al.  Effects of awareness diffusion and self-initiated awareness behavior on epidemic spreading - An approach based on multiplex networks , 2015, Communications in Nonlinear Science and Numerical Simulation.

[229]  Wei Wang,et al.  Critical phenomena of information spreading dynamics on networks with cliques , 2018, Physical Review E.

[230]  Viktor K. Prasanna,et al.  Computing competing cascades on signed networks , 2016, Social Network Analysis and Mining.

[231]  Jeremy Ginsberg,et al.  Detecting influenza epidemics using search engine query data , 2009, Nature.

[232]  Joel C Miller,et al.  Cocirculation of infectious diseases on networks. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[233]  Shuigeng Zhou,et al.  Epidemic spreading in weighted scale-free networks with community structure , 2009 .

[234]  Thilo Gross,et al.  Adaptive coevolutionary networks: a review , 2007, Journal of The Royal Society Interface.

[235]  Ali H. Sayed,et al.  Adaptive Networks , 2014, Proceedings of the IEEE.

[236]  Simon A. Levin,et al.  The dynamics of cocirculating influenza strains conferring partial cross-immunity , 1997, Journal of mathematical biology.

[237]  A. Barabasi,et al.  Impact of non-Poissonian activity patterns on spreading processes. , 2006, Physical review letters.

[238]  Alessandro Vespignani,et al.  Epidemic dynamics in finite size scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[239]  Alexandre Arenas,et al.  Clustering determines the dynamics of complex contagions in multiplex networks , 2016, Physical review. E.

[240]  A. Vespignani,et al.  Competition among memes in a world with limited attention , 2012, Scientific Reports.

[241]  K-I Goh,et al.  Threshold cascades with response heterogeneity in multiplex networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[242]  C. Buono,et al.  Epidemics in Partially Overlapped Multiplex Networks , 2013, PloS one.

[243]  N M Ferguson,et al.  Interactions of multiple strain pathogen diseases in the presence of coinfection, cross immunity, and arbitrary strain diversity. , 2008, Physical review letters.

[244]  H. White,et al.  Predictors of smoking cessation from adolescence into young adulthood. , 2001, Addictive behaviors.

[245]  Sergey Melnik,et al.  Accuracy of mean-field theory for dynamics on real-world networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[246]  M. Newman Spread of epidemic disease on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[247]  P. Kaye Infectious diseases of humans: Dynamics and control , 1993 .

[248]  Alessandro Vespignani,et al.  Characterising two-pathogen competition in spatially structured environments , 2014, Scientific Reports.

[249]  Mattia Frasca,et al.  Effect of individual behavior on epidemic spreading in activity-driven networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[250]  Tao Zhou,et al.  Measuring multiple evolution mechanisms of complex networks , 2014, Scientific Reports.

[251]  Tianshou Zhou,et al.  The influence of time delay on epidemic spreading under limited resources , 2018, Physica A: Statistical Mechanics and its Applications.

[252]  C. Bauch,et al.  Critical dynamics in population vaccinating behavior , 2017, Proceedings of the National Academy of Sciences.

[253]  D. Helbing,et al.  The Hidden Geometry of Complex, Network-Driven Contagion Phenomena , 2013, Science.

[254]  Tao Zhou,et al.  Destination choice game: A spatial interaction theory on human mobility , 2018, Scientific Reports.

[255]  N Azimi-Tafreshi,et al.  Cooperative epidemics on multiplex networks. , 2015, Physical review. E.

[256]  Mario Recker,et al.  Transient cross-reactive immune responses can orchestrate antigenic variation in malaria , 2004, Nature.

[257]  Jie Chang,et al.  The Role of Community Mixing Styles in Shaping Epidemic Behaviors in Weighted Networks , 2013, PloS one.

[258]  Huijuan Wang,et al.  Resilience of epidemics on networks , 2016, Chaos.

[259]  S. Fortunato,et al.  Resolution limit in community detection , 2006, Proceedings of the National Academy of Sciences.

[260]  Timothy M. Lenton,et al.  Potential analysis reveals changing number of climate states during the last 60 kyr , 2009 .

[261]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[262]  Pierre-André Noël,et al.  Time evolution of epidemic disease on finite and infinite networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[263]  Marián Boguñá,et al.  Epidemic spreading on interconnected networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[264]  Imran Rasul,et al.  Social Networks and Technology Adoption in Northern Mozambique , 2002 .

[265]  Chuang Liu,et al.  Coupling dynamics of epidemic spreading and information diffusion on complex networks , 2018, Applied Mathematics and Computation.

[266]  Jari Saramäki,et al.  Effects of temporal correlations on cascades: Threshold models on temporal networks , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[267]  Francisco J Pérez-Reche,et al.  Effects of variable-state neighborhoods for spreading synergystic processes on lattices. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[268]  Spain,et al.  Cascade Dynamics of Complex Propagation , 2005, physics/0504165.

[269]  Takehisa Hasegawa,et al.  Cascade dynamics on clustered network , 2010 .

[270]  Xiao Zhang,et al.  Localization and centrality in networks , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[271]  Harry Eugene Stanley,et al.  Calling patterns in human communication dynamics , 2013, Proceedings of the National Academy of Sciences.

[272]  Claudio Castellano,et al.  Relating topological determinants of complex networks to their spectral properties: structural and dynamical effects , 2017, 1703.10438.

[273]  Joel C. Miller,et al.  Percolation and epidemics in random clustered networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[274]  Fakhteh Ghanbarnejad,et al.  Exact solution of generalized cooperative susceptible-infected-removed (SIR) dynamics. , 2019, Physical review. E.

[275]  Ying-Cheng Lai,et al.  Universal model of individual and population mobility on diverse spatial scales , 2017, Nature Communications.

[276]  Hernán A. Makse,et al.  Influence maximization in complex networks through optimal percolation , 2015, Nature.

[277]  R. Pastor-Satorras,et al.  Generation of uncorrelated random scale-free networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[278]  Romualdo Pastor-Satorras,et al.  Distinct types of eigenvector localization in networks , 2015, Scientific Reports.

[279]  Yamir Moreno,et al.  The Dynamics of Protest Recruitment through an Online Network , 2011, Scientific reports.

[280]  Piet Van Mieghem,et al.  Domination-time dynamics in susceptible-infected-susceptible virus competition on networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[281]  Peng Sun,et al.  Decentralized resource allocation to control an epidemic: a game theoretic approach. , 2009, Mathematical biosciences.

[282]  Yamir Moreno,et al.  Cascading behaviour in complex socio-technical networks , 2013, J. Complex Networks.

[283]  Vasileios Karyotis,et al.  Malware Diffusion Models for Modern Complex Networks: Theory and Applications , 2016 .

[284]  Elvis H. W. Xu,et al.  Suppressed epidemics in multirelational networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[285]  Ming Tang,et al.  Efficient allocation of heterogeneous response times in information spreading process. , 2014, Chaos.

[286]  P. Van Mieghem,et al.  Epidemics in networks with nodal self-infection and the epidemic threshold. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[287]  Tao Sun,et al.  Media dependencies in a changing media environment: the case of the 2003 SARS epidemic in China , 2007, New Media Soc..

[288]  Ming Tang,et al.  Hybrid phase transitions of spreading dynamics in multiplex networks , 2018, Chinese Journal of Physics.

[289]  Mason A. Porter,et al.  Complex Contagions with Timers , 2017, Chaos.

[290]  Linyuan Lü,et al.  Spreading in online social networks: the role of social reinforcement. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[291]  Tao Zhou,et al.  Diversity of individual mobility patterns and emergence of aggregated scaling laws , 2012, Scientific Reports.

[292]  Peter G. Fennell,et al.  Limitations of discrete-time approaches to continuous-time contagion dynamics , 2016, Physical review. E.

[293]  Toshio Aoyagi,et al.  Scale-free structures emerging from co-evolution of a network and the distribution of a diffusive resource on it. , 2011, Physical review letters.

[294]  Lada A. Adamic,et al.  Social influence and the diffusion of user-created content , 2009, EC '09.

[295]  D. Campbell,et al.  Social Networks and Political Participation , 2013 .

[296]  S. Carpenter,et al.  Early-warning signals for critical transitions , 2009, Nature.

[297]  M. Newman Threshold effects for two pathogens spreading on a network. , 2005, Physical review letters.

[298]  J. Lockwood,et al.  Evolution of Concepts Associated with Soilborne Plant Pathogens , 1988 .

[299]  Quan-Hui Liu,et al.  Predicting the epidemic threshold of the susceptible-infected-recovered model , 2015, Scientific Reports.

[300]  Zhou Tao,et al.  Epidemic dynamics on complex networks , 2006 .

[301]  Thilo Gross,et al.  Analytical calculation of fragmentation transitions in adaptive networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[302]  Cécile Viboud,et al.  Reassessing Google Flu Trends Data for Detection of Seasonal and Pandemic Influenza: A Comparative Epidemiological Study at Three Geographic Scales , 2013, PLoS Comput. Biol..

[303]  Xin Jiang,et al.  The Role of Node Heterogeneity in the Coupled Spreading of Epidemics and Awareness , 2016, PloS one.

[304]  Vincent A. Traag,et al.  Complex Contagion of Campaign Donations , 2016, PloS one.

[305]  Marián Boguñá,et al.  Tuning clustering in random networks with arbitrary degree distributions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[306]  Sinan Aral,et al.  Exercise contagion in a global social network , 2017, Nature Communications.

[307]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[308]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[309]  Krishna P. Gummadi,et al.  Modeling Diffusion of Competing Products and Conventions in Social Media , 2014, NIPS 2014.

[310]  Xuzhen Zhu,et al.  Dynamics of social contagions with local trend imitation , 2017, Scientific Reports.

[311]  Yuan Yan Tang,et al.  A Bi-Virus Competing Spreading Model with Generic Infection Rates , 2018, IEEE Transactions on Network Science and Engineering.

[312]  Kristina Lerman,et al.  The Simple Rules of Social Contagion , 2013, Scientific Reports.

[313]  David Broder-Rodgers,et al.  Effects of local and global network connectivity on synergistic epidemics. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[314]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[315]  R. Pastor-Satorras,et al.  Epidemic spreading in correlated complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[316]  Ming Tang,et al.  Asymmetrically interacting spreading dynamics on complex layered networks , 2014, Scientific Reports.

[317]  Mason A. Porter,et al.  Author Correction: The physics of spreading processes in multilayer networks , 2016, 1604.02021.

[318]  N. M. Ferguson,et al.  Characterizing the symmetric equilibrium of multi-strain host-pathogen systems in the presence of cross immunity , 2005, Journal of mathematical biology.

[319]  Lin Wang,et al.  Spatial epidemiology of networked metapopulation: an overview , 2014, bioRxiv.

[320]  Yang Zou,et al.  Social contagions on multiplex networks with different reliability , 2018, Physica A: Statistical Mechanics and its Applications.

[321]  Christos Faloutsos,et al.  Winner takes all: competing viruses or ideas on fair-play networks , 2012, WWW.

[322]  James P. Gleeson,et al.  On Watts' cascade model with random link weights , 2012, J. Complex Networks.

[323]  Damon Centola,et al.  The Spread of Behavior in an Online Social Network Experiment , 2010, Science.

[324]  Yicheng Zhang,et al.  Dynamics of information diffusion and its applications on complex networks , 2016 .

[325]  Robin I. M. Dunbar Social Brain Hypothesis , 1998, Encyclopedia of Evolutionary Psychological Science.

[326]  Yicheng Zhang,et al.  Computational socioeconomics , 2019, Physics Reports.

[327]  Joel C. Miller,et al.  Complex contagions and hybrid phase transitions , 2016, J. Complex Networks.

[328]  H. Stanley,et al.  Effect of the interconnected network structure on the epidemic threshold. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[329]  James P. Gleeson,et al.  Cascades on a class of clustered random networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[330]  Ming Tang,et al.  Effects of weak ties on epidemic predictability on community networks , 2012, Chaos.

[331]  Jon Kleinberg,et al.  Differences in the mechanics of information diffusion across topics: idioms, political hashtags, and complex contagion on twitter , 2011, WWW.

[332]  Romualdo Pastor-Satorras,et al.  Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[333]  Qingchu Wu,et al.  Responsive immunization and intervention for infectious diseases in social networks , 2014, Chaos.

[334]  J. Borge-Holthoefer,et al.  Discrete-time Markov chain approach to contact-based disease spreading in complex networks , 2009, 0907.1313.

[335]  Claudio Castellano,et al.  Relevance of backtracking paths in recurrent-state epidemic spreading on networks , 2018, Physical Review. E.

[336]  Hai-Jun Zhou,et al.  Optimal Disruption of Complex Networks , 2016, 1605.09257.

[337]  Huaiping Zhu,et al.  An SIS Infection Model Incorporating Media Coverage , 2008 .

[338]  Zhen Wang,et al.  Dynamics of social contagions with heterogeneous adoption thresholds: crossover phenomena in phase transition , 2015, ArXiv.

[339]  Linda Richter,et al.  Behavioural strategies to reduce HIV transmission: how to make them work better , 2008, The Lancet.

[340]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[341]  Ming Tang,et al.  Synergistic interactions promote behavior spreading and alter phase transition on multiplex networks , 2018, Physical review. E.

[342]  Albert-László Barabási,et al.  The origin of bursts and heavy tails in human dynamics , 2005, Nature.

[343]  Attila Szolnoki,et al.  Coevolutionary Games - A Mini Review , 2009, Biosyst..

[344]  Alessandro Vespignani,et al.  Time varying networks and the weakness of strong ties , 2013, Scientific Reports.

[345]  J. Gleeson High-accuracy approximation of binary-state dynamics on networks. , 2011, Physical review letters.

[346]  Guofeng Li,et al.  Optimal allocation of resources for suppressing epidemic spreading on networks. , 2017, Physical review. E.

[347]  Marián Boguñá,et al.  Clustering in complex networks. II. Percolation properties. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[348]  Christos Faloutsos,et al.  Interacting viruses in networks: can both survive? , 2012, KDD.

[349]  Matteo Magnani,et al.  Spreading Processes in Multilayer Networks , 2014, IEEE Transactions on Network Science and Engineering.

[350]  Declan Butler,et al.  When Google got flu wrong , 2013, Nature.

[351]  Ming Tang,et al.  Social contagions on weighted networks , 2016, Physical review. E.

[352]  Marián Boguñá,et al.  Equivalence between Non-Markovian and Markovian Dynamics in Epidemic Spreading Processes. , 2017, Physical review letters.

[353]  Sophie Ahrens,et al.  Recommender Systems , 2012 .

[354]  Damon Centola An Experimental Study of Homophily in the Adoption of Health Behavior , 2011, Science.

[355]  M. Newman,et al.  Identifying the role that animals play in their social networks , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[356]  Sudip Samanta,et al.  Effects of awareness program and delay in the epidemic outbreak , 2017 .

[357]  Pejman Rohani,et al.  Tracking the dynamics of pathogen interactions: modeling ecological and immune-mediated processes in a two-pathogen single-host system. , 2007, Journal of theoretical biology.

[358]  Alessandro Vespignani,et al.  Measurability of the epidemic reproduction number in data-driven contact networks , 2018, Proceedings of the National Academy of Sciences.

[359]  Jean-Pierre Eckmann,et al.  Entropy of dialogues creates coherent structures in e-mail traffic. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[360]  Romualdo Pastor-Satorras,et al.  Effects of temporal correlations in social multiplex networks , 2016, Scientific Reports.

[361]  Hai-Jun Zhou,et al.  The Directed Dominating Set Problem: Generalized Leaf Removal and Belief Propagation , 2015, FAW.

[362]  Shlomo Havlin,et al.  Local structure can identify and quantify influential global spreaders in large scale social networks , 2015, Proceedings of the National Academy of Sciences.

[363]  SahnehFaryad Darabi,et al.  Generalized epidemic mean-field model for spreading processes over multilayer complex networks , 2013 .

[364]  Angélica S. Mata,et al.  Multiple transitions of the susceptible-infected-susceptible epidemic model on complex networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[365]  D Helbing,et al.  Connectivity disruption sparks explosive epidemic spreading. , 2016, Physical review. E.

[366]  M. Newman,et al.  Why social networks are different from other types of networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[367]  Richard J Hayes,et al.  Herpes simplex virus 2 infection increases HIV acquisition in men and women: systematic review and meta-analysis of longitudinal studies , 2006, AIDS.

[368]  Mark S. Granovetter,et al.  Threshold models of diffusion and collective behavior , 1983 .

[369]  V. Colizza,et al.  Analytical computation of the epidemic threshold on temporal networks , 2014, 1406.4815.

[370]  Peter Grassberger,et al.  Avalanche outbreaks emerging in cooperative contagions , 2015, Nature Physics.

[371]  Piet Van Mieghem,et al.  The N-intertwined SIS epidemic network model , 2011, Computing.

[372]  Guanrong Chen,et al.  Propagation of interacting diseases on multilayer networks. , 2018, Physical review. E.

[373]  Dawei Zhao,et al.  Statistical physics of vaccination , 2016, ArXiv.

[374]  Rick Durrett,et al.  Some features of the spread of epidemics and information on a random graph , 2010, Proceedings of the National Academy of Sciences.

[375]  Wei Wang,et al.  Complex contagions with social reinforcement from different layers and neighbors , 2018, Physica A: Statistical Mechanics and its Applications.

[376]  Petter Holme,et al.  Solving the Dynamic Correlation Problem of the Susceptible-Infected-Susceptible Model on Networks. , 2016, Physical review letters.

[377]  Mark S. Granovetter The Strength of Weak Ties , 1973, American Journal of Sociology.

[378]  Kim Sneppen,et al.  Locally self-organized quasicritical percolation in a multiple-disease model. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[379]  J. Gómez-Gardeñes,et al.  Explosive Contagion in Networks , 2016, Scientific Reports.

[380]  Yamir Moreno,et al.  Dynamics of rumor spreading in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[381]  K B Blyuss,et al.  Dynamics of vaccination in a time-delayed epidemic model with awareness. , 2017, Mathematical biosciences.

[382]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[383]  Matt J Keeling,et al.  Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[384]  A. K. Misra,et al.  Effect of awareness programs by media on the epidemic outbreaks: A mathematical model , 2013, Appl. Math. Comput..

[385]  Wei Wang,et al.  Optimal community structure for social contagions , 2018, 1805.00360.

[386]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[387]  Ariel BenYishay,et al.  Can Network Theory-Based Targeting Increase Technology Adoption? , 2018 .

[388]  Joel C Miller,et al.  Edge-based compartmental modelling for infectious disease spread , 2011, Journal of The Royal Society Interface.

[389]  Pejman Rohani,et al.  Statistical Inference for Multi-Pathogen Systems , 2011, PLoS Comput. Biol..

[390]  Lang Cao,et al.  Infection dynamics in structured populations with disease awareness based on neighborhood contact history , 2014, The European Physical Journal B.

[391]  Chinwendu Enyioha,et al.  Optimal vaccine allocation to control epidemic outbreaks in arbitrary networks , 2013, 52nd IEEE Conference on Decision and Control.

[392]  Hongyuan Zha,et al.  Correlated Cascades: Compete or Cooperate , 2015, AAAI.

[393]  Alexander Grey,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .

[394]  P. Grassberger,et al.  Outbreaks of coinfections: The critical role of cooperativity , 2013, 1307.2404.

[395]  Zonghua Liu,et al.  A unified framework of mutual influence between two pathogens in multiplex networks. , 2014, Chaos.

[396]  Tao Zhou,et al.  Epidemic spread in weighted scale-free networks , 2004, cond-mat/0408049.

[397]  Zhi-Dan Zhao,et al.  Scaling behavior of online human activity , 2012, ArXiv.

[398]  M E J Newman,et al.  Random graphs with clustering. , 2009, Physical review letters.

[399]  Joane Nagel,et al.  Resource Competition Theories , 1995 .

[400]  Romualdo Pastor-Satorras,et al.  Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks. , 2013, Physical review letters.

[401]  Bryan T Grenfell,et al.  Dynamics and selection of many-strain pathogens , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[402]  Michael Small,et al.  The Impacts of Subsidy Policies on Vaccination Decisions in Contact Networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[403]  Filippo Radicchi,et al.  Beyond the locally treelike approximation for percolation on real networks. , 2016, Physical review. E.

[404]  Zhi-Dan Zhao,et al.  Empirical analysis of online human dynamics , 2012 .

[405]  K. Eames,et al.  Modelling disease spread through random and regular contacts in clustered populations. , 2008, Theoretical population biology.

[406]  Marc Barthelemy,et al.  Spatial Networks , 2010, Encyclopedia of Social Network Analysis and Mining.

[407]  Bogang Jun,et al.  Collective Learning in China's Regional Economic Development Formations of Co-Inventors During the Dot-com Bubble in the Research Triangle Region , 2017, 1703.01369.

[408]  Ming Tang,et al.  Preferential imitation can invalidate targeted subsidy policies on seasonal-influenza diseases , 2017, Appl. Math. Comput..

[409]  Meeyoung Cha,et al.  Modeling the Adoption of Innovations in the Presence of Geographic and Media Influences , 2011, PloS one.

[410]  Ming Tang,et al.  Recovery rate affects the effective epidemic threshold with synchronous updating , 2016, Chaos.

[411]  Joel C. Miller Equivalence of several generalized percolation models on networks , 2016, Physical review. E.

[412]  Kim Sneppen,et al.  A Minimal Model for Multiple Epidemics and Immunity Spreading , 2010, PloS one.

[413]  Xuzhen Zhu,et al.  Optimal imitation capacity and crossover phenomenon in the dynamics of social contagions , 2018, Journal of Statistical Mechanics: Theory and Experiment.

[414]  M. Newman Properties of highly clustered networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[415]  Alessandro Ingrosso,et al.  The patient-zero problem with noisy observations , 2014, 1408.0907.

[416]  T. Geisel,et al.  Natural human mobility patterns and spatial spread of infectious diseases , 2011, 1103.6224.

[417]  Elizabeth Hunter Review of Complex Spreading Phenomena in Social Systems , 2019 .

[418]  Mason A. Porter,et al.  Multi-Stage Complex Contagions , 2011, Chaos.

[419]  Joel C. Miller Spread of infectious disease through clustered populations , 2008, Journal of The Royal Society Interface.

[420]  Lev Muchnik,et al.  Identifying influential spreaders in complex networks , 2010, 1001.5285.

[421]  Michael A. Andrews,et al.  Disease Interventions Can Interfere with One Another through Disease-Behaviour Interactions , 2015, PLoS Comput. Biol..

[422]  Chuanji Fu,et al.  Center of mass in complex networks , 2017, Scientific Reports.

[423]  Mason A. Porter,et al.  Synergistic effects in threshold models on networks , 2017, Chaos.

[424]  Konstantin B Blyuss,et al.  A Class of Pairwise Models for Epidemic Dynamics on Weighted Networks , 2012, Bulletin of Mathematical Biology.

[425]  Jingwen Zhang,et al.  Support or competition? How online social networks increase physical activity: A randomized controlled trial☆ , 2016, Preventive medicine reports.

[426]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[427]  Francesca Colaiori,et al.  Mutually cooperative epidemics on power-law networks , 2017, Physical review. E.

[428]  C. Bauch Imitation dynamics predict vaccinating behaviour , 2005, Proceedings of the Royal Society B: Biological Sciences.

[429]  Peter Sheridan Dodds,et al.  Information cascades on degree-correlated random networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[430]  J. Gleeson Binary-state dynamics on complex networks: pair approximation and beyond , 2012, 1209.2983.

[431]  Lidia A. Braunstein,et al.  Temporal Percolation of the Susceptible Network in an Epidemic Spreading , 2012, PloS one.

[432]  Martin A. Nowak,et al.  Antigenic oscillations and shifting immunodominance in HIV-1 infections , 1995, Nature.

[433]  R. Pastor-Satorras,et al.  Langevin approach for the dynamics of the contact process on annealed scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[434]  Or Givan,et al.  Predicting epidemic thresholds on complex networks: limitations of mean-field approaches. , 2011, Journal of theoretical biology.

[435]  Huaiping Zhu,et al.  Media/psychological impact on multiple outbreaks of emerging infectious diseases , 2007 .

[436]  Ming-Can Fan,et al.  Ultrafast synchronization via local observation , 2017, New Journal of Physics.

[437]  A. Perliger,et al.  Social Network Analysis in the Study of Terrorism and Political Violence , 2011, PS: Political Science & Politics.

[438]  Joshua L. Payne,et al.  Analysis of a threshold model of social contagion on degree-correlated networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[439]  Tao Zhou,et al.  Strong ties promote the epidemic prevalence in susceptible–infected–susceptible spreading dynamics , 2016 .

[440]  Fabrizio Lillo,et al.  Optimal information diffusion in stochastic block models , 2016, Physical review. E.

[441]  Ming Tang,et al.  Impacts of complex behavioral responses on asymmetric interacting spreading dynamics in multiplex networks , 2015, Scientific Reports.

[442]  D. Watts,et al.  A generalized model of social and biological contagion. , 2005, Journal of theoretical biology.

[443]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[444]  Jian Liu,et al.  Dynamics of competing ideas in complex social systems , 2011, ArXiv.

[445]  L. Hébert-Dufresne,et al.  Propagation dynamics on networks featuring complex topologies. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[446]  I. Kiss,et al.  Exact epidemic models on graphs using graph-automorphism driven lumping , 2010, Journal of mathematical biology.

[447]  Jürgen Kurths,et al.  Evidence for a bimodal distribution in human communication , 2010, Proceedings of the National Academy of Sciences.

[448]  Ming Tang,et al.  Social contagions on time-varying community networks , 2016, Physical review. E.

[449]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[450]  Joel C. Miller A note on a paper by Erik Volz: SIR dynamics in random networks , 2009, Journal of mathematical biology.

[451]  R. Pastor-Satorras,et al.  Activity driven modeling of time varying networks , 2012, Scientific Reports.

[452]  M. Macy,et al.  Complex Contagions and the Weakness of Long Ties1 , 2007, American Journal of Sociology.

[453]  M. Keeling,et al.  Modeling Infectious Diseases in Humans and Animals , 2007 .

[454]  H. Stanley,et al.  Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. , 2007, Physical review letters.

[455]  M A Nowak,et al.  Superinfection and the evolution of parasite virulence. , 1994, Proceedings. Biological sciences.

[456]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[457]  John Kelly,et al.  Investigating the Observability of Complex Contagion in Empirical Social Networks , 2021, ICWSM.

[458]  R. May,et al.  Systemic risk: the dynamics of model banking systems , 2010, Journal of The Royal Society Interface.

[459]  Harry Eugene Stanley,et al.  Epidemics on Interconnected Networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[460]  Li Chen,et al.  Persistent spatial patterns of interacting contagions , 2018, Physical review. E.

[461]  Chinwendu Enyioha,et al.  Distributed resource allocation for control of spreading processes , 2015, 2015 European Control Conference (ECC).

[462]  Wei Wang,et al.  Double transition of information spreading in a two-layered network. , 2018, Chaos.

[463]  Sune Lehmann,et al.  Spreading in Social Systems: Reflections , 2018, ArXiv.

[464]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[465]  Petter Holme,et al.  Bursty Communication Patterns Facilitate Spreading in a Threshold-Based Epidemic Dynamics , 2012, PloS one.

[466]  Bambi Hu,et al.  Epidemic spreading in community networks , 2005 .

[467]  Alessandro Vespignani,et al.  Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. , 2003, Physical review letters.

[468]  Samir Suweis,et al.  Collapse of resilience patterns in generalized Lotka-Volterra dynamics and beyond. , 2016, Physical review. E.

[469]  Joan Saldaña,et al.  Tuning the overlap and the cross-layer correlations in two-layer networks: Application to a susceptible-infectious-recovered model with awareness dissemination , 2018, Physical review. E.

[470]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[471]  Martin A. Nowak,et al.  Superinfection and the evolution of parasite virulence , 1994, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[472]  Xinchu Fu,et al.  Modelling of discrete-time SIS models with awareness interactions on degree-uncorrelated networks , 2011 .

[473]  Wilfred Otten,et al.  Applications of percolation theory to fungal spread with synergy , 2012, Journal of The Royal Society Interface.

[474]  Tao Zhou,et al.  Interactive social contagions and co-infections on complex networks. , 2018, Chaos.

[475]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[476]  Mason A. Porter,et al.  Dynamical Systems on Networks: A Tutorial , 2014, ArXiv.

[477]  Wei Wang,et al.  Social contagions on interdependent lattice networks , 2017, Scientific Reports.

[478]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[479]  Aaron Clauset,et al.  Scale-free networks are rare , 2018, Nature Communications.

[480]  Lidia A. Braunstein,et al.  Effects of time-delays in the dynamics of social contagions , 2018 .

[481]  Yichuan Jiang,et al.  Cross-layers cascade in multiplex networks , 2014, Auton. Agents Multi Agent Syst..

[482]  Yasuhiro Takeuchi,et al.  Modeling the effect of time delay in budget allocation to control an epidemic through awareness , 2017 .

[483]  M. A. Muñoz,et al.  Griffiths phases on complex networks. , 2010, Physical review letters.

[484]  N. Ferguson,et al.  Ecological and immunological determinants of influenza evolution , 2003, Nature.

[485]  Brian Karrer,et al.  Message passing approach for general epidemic models. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[486]  Alessandro Vespignani,et al.  Modeling Users' Activity on Twitter Networks: Validation of Dunbar's Number , 2011, PloS one.

[487]  Harry Eugene Stanley,et al.  Catastrophic cascade of failures in interdependent networks , 2009, Nature.

[488]  Ming Tang,et al.  Suppressing disease spreading by using information diffusion on multiplex networks , 2016, Scientific Reports.

[489]  T. Lenton Early warning of climate tipping points , 2011 .

[490]  Li-Jie Zhang,et al.  Contagion on complex networks with persuasion , 2016, Scientific Reports.

[491]  Tao Zhou,et al.  Impact of Heterogeneous Human Activities on Epidemic Spreading , 2011, ArXiv.

[492]  K. Goh,et al.  Spreading dynamics following bursty human activity patterns. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[493]  Hana Ross,et al.  The importance of peer effects, cigarette prices and tobacco control policies for youth smoking behavior. , 2005, Journal of health economics.

[494]  Naoki Masuda,et al.  A Guide to Temporal Networks , 2016, Series on Complexity Science.

[495]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[496]  A. Barabasi,et al.  Universal resilience patterns in complex networks , 2016, Nature.

[497]  Alessandro Vespignani,et al.  Weighted evolving networks: coupling topology and weight dynamics. , 2004, Physical review letters.

[498]  Carlos Castillo-Chavez,et al.  Competitive Exclusion in Gonorrhea Models and Other Sexually Transmitted Diseases , 1996, SIAM J. Appl. Math..

[499]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[500]  Bing-Hong Wang,et al.  Braess's Paradox in Epidemic Game: Better Condition Results in Less Payoff , 2013, Scientific Reports.

[501]  Paul Resnick,et al.  Recommender systems , 1997, CACM.

[502]  Sergio Gómez,et al.  Competing spreading processes on multiplex networks: awareness and epidemics , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[503]  T. Geisel,et al.  Forecast and control of epidemics in a globalized world. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[504]  Daniel I. S. Rosenbloom,et al.  Imitation dynamics of vaccination behaviour on social networks , 2011, Proceedings of the Royal Society B: Biological Sciences.

[505]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[506]  Santo Fortunato,et al.  Community detection in networks: A user guide , 2016, ArXiv.

[507]  Jari Saramäki,et al.  Temporal Networks , 2011, Encyclopedia of Social Network Analysis and Mining.

[508]  Márton Karsai,et al.  Nonequilibrium phase transitions and finite-size scaling in weighted scale-free networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[509]  Tanja Popovic,et al.  Mutator clones of Neisseria meningitidis in epidemic serogroup A disease , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[510]  George J. Pappas,et al.  Optimal resource allocation for containing epidemics on time-varying networks , 2015, 2015 49th Asilomar Conference on Signals, Systems and Computers.

[511]  Guido Caldarelli,et al.  Scale-Free Networks , 2007 .

[512]  Mark E. J. Newman,et al.  Competing epidemics on complex networks , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[513]  D. Lazer,et al.  The Parable of Google Flu: Traps in Big Data Analysis , 2014, Science.

[514]  Feng Fu,et al.  Co-diffusion of social contagions , 2018, New Journal of Physics.

[515]  N. Christakis,et al.  SUPPLEMENTARY ONLINE MATERIAL FOR: The Collective Dynamics of Smoking in a Large Social Network , 2022 .

[516]  Thilo Gross,et al.  Epidemic dynamics on an adaptive network. , 2005, Physical review letters.

[517]  Guanrong Chen,et al.  Propagation Dynamics on Complex Networks: Models, Methods and Stability Analysis , 2014 .

[518]  David A. Rand,et al.  Correlation Equations and Pair Approximations for Spatial Ecologies , 1999 .

[519]  K-I Goh,et al.  Multiplexity-facilitated cascades in networks. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.