1
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Huang Z, Shu X, Xuan Q, Ruan Z. Epidemic spreading under game-based self-quarantine behaviors: The different effects of local and global information. CHAOS (WOODBURY, N.Y.) 2024; 34:013112. [PMID: 38198677 DOI: 10.1063/5.0180484] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Accepted: 12/12/2023] [Indexed: 01/12/2024]
Abstract
During the outbreak of an epidemic, individuals may modify their behaviors in response to external (including local and global) infection-related information. However, the difference between local and global information in influencing the spread of diseases remains inadequately explored. Here, we study a simple epidemic model that incorporates the game-based self-quarantine behavior of individuals, taking into account the influence of local infection status, global disease prevalence, and node heterogeneity (non-identical degree distribution). Our findings reveal that local information can effectively contain an epidemic, even with only a small proportion of individuals opting for self-quarantine. On the other hand, global information can cause infection evolution curves shaking during the declining phase of an epidemic, owing to the synchronous release of nodes with the same degree from the quarantined state. In contrast, the releasing pattern under the local information appears to be more random. This shaking phenomenon can be observed in various types of networks associated with different characteristics. Moreover, it is found that under the proposed game-epidemic framework, a disease is more difficult to spread in heterogeneous networks than in homogeneous networks, which differs from conventional epidemic models.
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Affiliation(s)
- Zegang Huang
- Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China
- Binjiang Cyberspace Security Institute of ZJUT, Hangzhou 310051, China
| | - Xincheng Shu
- Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China
- Binjiang Cyberspace Security Institute of ZJUT, Hangzhou 310051, China
| | - Qi Xuan
- Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China
- Binjiang Cyberspace Security Institute of ZJUT, Hangzhou 310051, China
| | - Zhongyuan Ruan
- Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China
- Binjiang Cyberspace Security Institute of ZJUT, Hangzhou 310051, China
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2
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Yu H, Xue B, Zhang J, Liu RR, Liu Y, Meng F. Opinion cascade under perception bias in social networks. CHAOS (WOODBURY, N.Y.) 2023; 33:113107. [PMID: 37909902 DOI: 10.1063/5.0172121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2023] [Accepted: 10/09/2023] [Indexed: 11/03/2023]
Abstract
Opinion cascades, initiated by active opinions, offer a valuable avenue for exploring the dynamics of consensus and disagreement formation. Nevertheless, the impact of biased perceptions on opinion cascade, arising from the balance between global information and locally accessible information within network neighborhoods, whether intentionally or unintentionally, has received limited attention. In this study, we introduce a threshold model to simulate the opinion cascade process within social networks. Our findings reveal that consensus emerges only when the collective stubbornness of the population falls below a critical threshold. Additionally, as stubbornness decreases, we observe a higher prevalence of first-order and second-order phase transitions between consensus and disagreement. The emergence of disagreement can be attributed to the formation of echo chambers, which are tightly knit communities where agents' biased perceptions of active opinions are lower than their stubbornness, thus hindering the erosion of active opinions. This research establishes a valuable framework for investigating the relationship between perception bias and opinion formation, providing insights into addressing disagreement in the presence of biased information.
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Affiliation(s)
- Hao Yu
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
| | - Bin Xue
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
| | - Jianlin Zhang
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
| | - Run-Ran Liu
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
| | - Yu Liu
- International Academic Center of Complex Systems, Beijing Normal University, Zhuhai 519087, China
| | - Fanyuan Meng
- Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, Zhejiang, China
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3
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Kobayashi T. Social contagion induced by uncertain information. Phys Rev E 2023; 107:064301. [PMID: 37464698 DOI: 10.1103/physreve.107.064301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2022] [Accepted: 05/23/2023] [Indexed: 07/20/2023]
Abstract
Information and individual activities often spread globally through the network of social ties. While social contagion phenomena have been extensively studied within the framework of threshold models, it is common to make an assumption that may be violated in reality: each individual can observe the neighbors' states without error. Here, we analyze the dynamics of global cascades under uncertainty in an otherwise standard threshold model. Each individual uses statistical inference to estimate the probability distribution of the number of active neighbors when deciding whether to be active, which gives a probabilistic threshold rule. Unlike the deterministic threshold model, the spreading process is generally nonmonotonic, as the inferred distribution of neighbors' states may be updated as a new signal arrives. We find that social contagion may occur as a self-fulfilling event in that misperception may trigger a cascade in regions where cascades would never occur under certainty.
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Affiliation(s)
- Teruyoshi Kobayashi
- Department of Economics, Center for Computational Social Science, Kobe University, Kobe 657-8501, Japan
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4
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Li W, Nie Y, Li W, Chen X, Su S, Wang W. Two competing simplicial irreversible epidemics on simplicial complex. CHAOS (WOODBURY, N.Y.) 2022; 32:093135. [PMID: 36182379 DOI: 10.1063/5.0100315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 08/26/2022] [Indexed: 06/16/2023]
Abstract
Higher-order interactions have significant implications for the dynamics of competing epidemic spreads. In this paper, a competing spread model for two simplicial irreversible epidemics (i.e., susceptible-infected-removed epidemics) on higher-order networks is proposed. The simplicial complexes are based on synthetic (including homogeneous and heterogeneous) and real-world networks. The spread process of two epidemics is theoretically analyzed by extending the microscopic Markov chain approach. When the two epidemics have the same 2-simplex infection rate and the 1-simplex infection rate of epidemic A ( λ) is fixed at zero, an increase in the 1-simplex infection rate of epidemic B ( λ) causes a transition from continuous growth to sharp growth in the spread of epidemic B with λ. When λ > 0, the growth of epidemic B is always continuous. With the increase of λ, the outbreak threshold of epidemic B is delayed. When the difference in 1-simplex infection rates between the two epidemics reaches approximately three times, the stronger side obviously dominates. Otherwise, the coexistence of the two epidemics is always observed. When the 1-simplex infection rates are symmetrical, the increase in competition will accelerate the spread process and expand the spread area of both epidemics; when the 1-simplex infection rates are asymmetrical, the spread area of one epidemic increases with an increase in the 1-simplex infection rate from this epidemic while the other decreases. Finally, the influence of 2-simplex infection rates on the competing spread is discussed. An increase in 2-simplex infection rates leads to sharp growth in one of the epidemics.
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Affiliation(s)
- Wenjie Li
- School of Public Health and Management, Chongqing Medical University, Chongqing 400016, China
| | - Yanyi Nie
- School of Public Health and Management, Chongqing Medical University, Chongqing 400016, China
| | - Wenyao Li
- College of Computer Science, Sichuan University, Chengdu 610065, China
| | - Xiaolong Chen
- School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics, Chengdu 611130, China
| | - Sheng Su
- School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu 611713, China
| | - Wei Wang
- School of Public Health and Management, Chongqing Medical University, Chongqing 400016, China
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5
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Brandl HB, Pruessner JC, Farine DR. The social transmission of stress in animal collectives. Proc Biol Sci 2022; 289:20212158. [PMID: 35538776 PMCID: PMC9091854 DOI: 10.1098/rspb.2021.2158] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Accepted: 03/18/2022] [Indexed: 01/04/2023] Open
Abstract
The stress systems are powerful mediators between the organism's systemic dynamic equilibrium and changes in its environment beyond the level of anticipated fluctuations. Over- or under-activation of the stress systems' responses can impact an animal's health, survival and reproductive success. While physiological stress responses and their influence on behaviour and performance are well understood at the individual level, it remains largely unknown whether-and how-stressed individuals can affect the stress systems of other group members, and consequently their collective behaviour. Stressed individuals could directly signal the presence of a stressor (e.g. via an alarm call or pheromones), or an acute or chronic activation of the stress systems could be perceived by others (as an indirect cue) and spread via social contagion. Such social transmission of stress responses could then amplify the effects of stressors by impacting social interactions, social dynamics and the collective performance of groups. As the neuroendocrine pathways of the stress response are highly conserved among vertebrates, transmission of physiological stress states could be more widespread among non-human animals than previously thought. We therefore suggest that identifying the extent to which stress transmission modulates animal collectives represents an important research avenue.
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Affiliation(s)
- Hanja B. Brandl
- Centre for the Advanced Study of Collective Behaviour, University of Konstanz, 78457 Konstanz, Germany
- Department of Collective Behaviour, Max Planck Institute of Animal Behavior, 78457 Konstanz, Germany
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, 8057 Zurich, Switzerland
| | - Jens C. Pruessner
- Centre for the Advanced Study of Collective Behaviour, University of Konstanz, 78457 Konstanz, Germany
- Department of Psychology, University of Konstanz, 78457 Konstanz, Germany
| | - Damien R. Farine
- Centre for the Advanced Study of Collective Behaviour, University of Konstanz, 78457 Konstanz, Germany
- Department of Collective Behaviour, Max Planck Institute of Animal Behavior, 78457 Konstanz, Germany
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, 8057 Zurich, Switzerland
- Division of Ecology and Evolution, Research School of Biology, Australian National University, Canberra, ACT 2600, Australia
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6
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MEBC: social network immunization via motif-based edge-betweenness centrality. Knowl Inf Syst 2022. [DOI: 10.1007/s10115-022-01671-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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7
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Keating LA, Gleeson JP, O'Sullivan DJP. Multitype branching process method for modeling complex contagion on clustered networks. Phys Rev E 2022; 105:034306. [PMID: 35428098 DOI: 10.1103/physreve.105.034306] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Accepted: 01/21/2022] [Indexed: 06/14/2023]
Abstract
Complex contagion adoption dynamics are characterized by a node being more likely to adopt after multiple network neighbors have adopted. We show how to construct multitype branching processes to approximate complex contagion adoption dynamics on networks with clique-based clustering. This involves tracking the evolution of a cascade via different classes of clique motifs that account for the different numbers of active, inactive, and removed nodes. This discrete-time model assumes that active nodes become immediately and certainly removed in the next time step. This description allows for extensive Monte Carlo simulations (which are faster than network-based simulations), accurate analytical calculation of cascade sizes, determination of critical behavior, and other quantities of interest.
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Affiliation(s)
- Leah A Keating
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
| | - James P Gleeson
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
| | - David J P O'Sullivan
- MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
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8
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de Oliveira JF, Marques-Neto HT, Karsai M. Measuring the effects of repeated and diversified influence mechanism for information adoption on Twitter. SOCIAL NETWORK ANALYSIS AND MINING 2021. [DOI: 10.1007/s13278-021-00844-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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9
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Peralta AF, Neri M, Kertész J, Iñiguez G. Effect of algorithmic bias and network structure on coexistence, consensus, and polarization of opinions. Phys Rev E 2021; 104:044312. [PMID: 34781537 DOI: 10.1103/physreve.104.044312] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2021] [Accepted: 10/04/2021] [Indexed: 11/07/2022]
Abstract
Individuals of modern societies share ideas and participate in collective processes within a pervasive, variable, and mostly hidden ecosystem of content filtering technologies that determine what information we see online. Despite the impact of these algorithms on daily life and society, little is known about their effect on information transfer and opinion formation. It is thus unclear to what extent algorithmic bias has a harmful influence on collective decision-making, such as a tendency to polarize debate. Here we introduce a general theoretical framework to systematically link models of opinion dynamics, social network structure, and content filtering. We showcase the flexibility of our framework by exploring a family of binary-state opinion dynamics models where information exchange lies in a spectrum from pairwise to group interactions. All models show an opinion polarization regime driven by algorithmic bias and modular network structure. The role of content filtering is, however, surprisingly nuanced; for pairwise interactions it leads to polarization, while for group interactions it promotes coexistence of opinions. This allows us to pinpoint which social interactions are robust against algorithmic bias, and which ones are susceptible to bias-enhanced opinion polarization. Our framework gives theoretical ground for the development of heuristics to tackle harmful effects of online bias, such as information bottlenecks, echo chambers, and opinion radicalization.
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Affiliation(s)
- Antonio F Peralta
- Department of Network and Data Science, Central European University, A-1100 Vienna, Austria
| | - Matteo Neri
- Department of Network and Data Science, Central European University, A-1100 Vienna, Austria
| | - János Kertész
- Department of Network and Data Science, Central European University, A-1100 Vienna, Austria.,Complexity Science Hub, A-1080 Vienna, Austria
| | - Gerardo Iñiguez
- Department of Network and Data Science, Central European University, A-1100 Vienna, Austria.,Department of Computer Science, Aalto University School of Science, FI-00076 Aalto, Finland.,Centro de Ciencias de la Complejidad, Universidad Nacional Autonóma de México, 04510 Ciudad de México, Mexico
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10
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Ruan Z, Yu B, Zhang X, Xuan Q. Role of lurkers in threshold-driven information spreading dynamics. Phys Rev E 2021; 104:034308. [PMID: 34654143 DOI: 10.1103/physreve.104.034308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2020] [Accepted: 09/09/2021] [Indexed: 11/07/2022]
Abstract
The threshold model as a classical paradigm for studying information spreading processes has been well studied. The main focuses are on how the underlying social network structure or the size of initial seeds can affect the cascading dynamics. However, the influence of node characteristics has been largely ignored. Here, inspired by empirical observations, we extend the threshold model by taking into account lurking nodes, who rarely interact with their neighbors. In particular, we consider two different scenarios: (i) Lurkers are absolutely silent and never interact with others and (ii) lurkers intermittently interact with their neighborhood with an activity rate p. In the first case, we demonstrate that lurkers may reduce the effective average degree of the underlying network, playing a dual role in spreading dynamics. In the latter case, we find that the stochastic dynamic behavior of lurkers could significantly promote the spread of information. Concretely, slightly raising the activity rate p of lurkers may result in a remarkable increase in the final cascade size. Further increasing p could make nodes become more stable on average, while it is still easy to observe global cascades due to the fluctuations of the effective degree of nodes.
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Affiliation(s)
- Zhongyuan Ruan
- Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China
| | - Bin Yu
- Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China
| | - Xiyun Zhang
- Department of Physics, Jinan University, Guangzhou, Guangdong 510632, China
| | - Qi Xuan
- Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China
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11
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Carta A, Sperduti A, Bacciu D. Encoding-based memory for recurrent neural networks. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2021.04.051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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12
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Krause J, Romanczuk P, Cracco E, Arlidge W, Nassauer A, Brass M. Collective rule-breaking. Trends Cogn Sci 2021; 25:1082-1095. [PMID: 34493441 DOI: 10.1016/j.tics.2021.08.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Revised: 08/06/2021] [Accepted: 08/09/2021] [Indexed: 10/20/2022]
Abstract
Rules form an important part of our everyday lives. Here we explore the role of social influence in rule-breaking. In particular, we identify some of the cognitive mechanisms underlying rule-breaking and propose approaches for how they can be scaled up to the level of groups or crowds to better understand the emergence of collective rule-breaking. Social contagion plays an important role in such processes and different dynamics such as linear or rapid nonlinear spreading can have important consequences for interventions in rule-breaking. A closer integration of cognitive psychology, microsociology and mathematical modelling will be key to a deeper understanding of collective rule-breaking to turn this field of research into a predictive science.
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Affiliation(s)
- Jens Krause
- Faculty of Life Sciences, Humboldt-Universität zu Berlin, Invalidenstrasse 42, 10115 Berlin, Germany; Department of Biology and Ecology of Fishes, Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Müggelseedamm 310, 12587 Berlin, Germany.
| | - Pawel Romanczuk
- Institute for Theoretical Biology, Department of Biology, Humboldt-Universität zu Berlin, Philippstraße 13, 10115 Berlin, Germany; Bernstein Center for Computational Neuroscience Berlin, Philippstr. 13, 10115 Berlin, Germany
| | - Emiel Cracco
- Department of Experimental Psychology, Ghent University, Ghent, Belgium
| | - William Arlidge
- Department of Biology and Ecology of Fishes, Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Müggelseedamm 310, 12587 Berlin, Germany
| | - Anne Nassauer
- Department of Sociology, John F. Kennedy Institute, Freie Universität Berlin, Lansstrasse 7-9, 14195 Berlin, Germany
| | - Marcel Brass
- Department of Experimental Psychology, Ghent University, Ghent, Belgium; Berlin School of Mind and Brain/Department of Psychology, Humboldt-Universität zu Berlin, Berlin, Germany
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13
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Kahana D, Yamin D. Accounting for the spread of vaccination behavior to optimize influenza vaccination programs. PLoS One 2021; 16:e0252510. [PMID: 34086772 PMCID: PMC8177529 DOI: 10.1371/journal.pone.0252510] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2021] [Accepted: 05/06/2021] [Indexed: 12/21/2022] Open
Abstract
Vaccination is the most efficient means of preventing influenza infection and its complications. While previous studies have considered the externalities of vaccination that arise from indirect protection against influenza infection, they have often neglected another key factor-the spread of vaccination behavior among social contacts. We modeled influenza vaccination as a socially contagious process. Our model uses a contact network that we developed based on aggregated and anonymized mobility data from the cellphone devices of ~1.8 million users in Israel. We calibrated the model to high-quality longitudinal data of weekly influenza vaccination uptake and influenza diagnoses over seven years. We demonstrate how a simple coupled-transmission model accurately captures the spatiotemporal patterns of both influenza vaccination uptake and influenza incidence. Taking the identified complex underlying dynamics of these two processes into account, our model determined the optimal timing of influenza vaccination programs. Our simulation shows that in regions where high vaccination coverage is anticipated, vaccination uptake would be more rapid. Thus, our model suggests that vaccination programs should be initiated later in the season, to mitigate the effect of waning immunity from the vaccine. Our simulations further show that optimally timed vaccination programs can substantially reduce disease transmission without increasing vaccination uptake.
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Affiliation(s)
- Dor Kahana
- Department of Industrial Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
| | - Dan Yamin
- Department of Industrial Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
- Center for Combatting Pandemics, Tel Aviv University, Tel Aviv, Israel
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14
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Smolyak A, Levy O, Vodenska I, Buldyrev S, Havlin S. Mitigation of cascading failures in complex networks. Sci Rep 2020; 10:16124. [PMID: 32999338 PMCID: PMC7528121 DOI: 10.1038/s41598-020-72771-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2020] [Accepted: 09/04/2020] [Indexed: 11/09/2022] Open
Abstract
Cascading failures in many systems such as infrastructures or financial networks can lead to catastrophic system collapse. We develop here an intuitive, powerful and simple-to-implement approach for mitigation of cascading failures on complex networks based on local network structure. We offer an algorithm to select critical nodes, the protection of which ensures better survival of the network. We demonstrate the strength of our approach compared to various standard mitigation techniques. We show the efficacy of our method on various network structures and failure mechanisms, and finally demonstrate its merit on an example of a real network of financial holdings.
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Affiliation(s)
- Alex Smolyak
- Department of Physics, Bar-Ilan University, 52900, Ramat-Gan, Israel.
| | - Orr Levy
- Department of Physics, Bar-Ilan University, 52900, Ramat-Gan, Israel
| | - Irena Vodenska
- Department of Administrative Sciences, Metropolitan College, Boston University, 1010 Commonwealth Avenue, Boston, MA, 02215, USA
| | - Sergey Buldyrev
- Department of Physics, Yeshiva University, 500 West 185th Street, New York, 10033, USA
| | - Shlomo Havlin
- Department of Physics, Bar-Ilan University, 52900, Ramat-Gan, Israel
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15
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Ruan Z, Yu B, Shu X, Zhang Q, Xuan Q. The impact of malicious nodes on the spreading of false information. CHAOS (WOODBURY, N.Y.) 2020; 30:083101. [PMID: 32872799 DOI: 10.1063/5.0005105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Accepted: 07/13/2020] [Indexed: 06/11/2023]
Abstract
Increasing empirical evidence in recent years has shown that bots or malicious users in a social network play a critical role in the propagation of false information, while a theoretical modeling of such a problem has been largely ignored. In this paper, applying a simple contagion model, we study the effect of malicious nodes on the spreading of false information by incorporating the smart nodes who perform better than normal nodes in discerning false information. The malicious nodes, however, will always repost (or adopt) the false message as long as they receive it. We show analytically that, for a random distribution of malicious nodes, there is a critical number of malicious nodes above which the false information could outbreak in a random network. We further study three different distribution strategies of selecting malicious nodes for false information spreading. We find that malicious nodes that have large degrees, or are tightly connected, can enhance the spread. However, when they are close to the smart nodes, the spreading of false information can either be promoted or inhibited, depending on the network structure.
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Affiliation(s)
- Zhongyuan Ruan
- Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China
| | - Bin Yu
- Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China
| | - Xincheng Shu
- Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China
| | - Qingpeng Zhang
- School of Data Science, City University of Hong Kong, Hong Kong 999077, China
| | - Qi Xuan
- Institute of Cyberspace Security, Zhejiang University of Technology, Hangzhou 310023, China
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16
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Unicomb S, Iñiguez G, Kertész J, Karsai M. Reentrant phase transitions in threshold driven contagion on multiplex networks. Phys Rev E 2019; 100:040301. [PMID: 31770919 DOI: 10.1103/physreve.100.040301] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2018] [Indexed: 11/07/2022]
Abstract
Models of threshold driven contagion explain the cascading spread of information, behavior, systemic risk, and epidemics on social, financial, and biological networks. At odds with empirical observations, these models predict that single-layer unweighted networks become resistant to global cascades after reaching sufficient connectivity. We investigate threshold driven contagion on weight heterogeneous multiplex networks and show that they can remain susceptible to global cascades at any level of connectivity, and with increasing edge density pass through alternating phases of stability and instability in the form of reentrant phase transitions of contagion. Our results provide a theoretical explanation for the observation of large-scale contagion in highly connected but heterogeneous networks.
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Affiliation(s)
- Samuel Unicomb
- Université de Lyon, ENS de Lyon, INRIA, CNRS, UMR 5668, IXXI, F-69364 Lyon, France
| | - Gerardo Iñiguez
- Department of Network and Data Science, Central European University, H-1051 Budapest, Hungary.,Department of Computer Science, Aalto University School of Science, FIN-00076 Aalto, Finland.,IIMAS, Universidad Nacional Autonóma de México, 01000 Ciudad de México, Mexico
| | - János Kertész
- Department of Network and Data Science, Central European University, H-1051 Budapest, Hungary
| | - Márton Karsai
- Université de Lyon, ENS de Lyon, INRIA, CNRS, UMR 5668, IXXI, F-69364 Lyon, France.,Department of Network and Data Science, Central European University, H-1051 Budapest, Hungary
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17
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Wang W, Liu QH, Liang J, Hu Y, Zhou T. Coevolution spreading in complex networks. PHYSICS REPORTS 2019; 820:1-51. [PMID: 32308252 PMCID: PMC7154519 DOI: 10.1016/j.physrep.2019.07.001] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Revised: 06/27/2019] [Accepted: 07/18/2019] [Indexed: 05/03/2023]
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.
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Affiliation(s)
- Wei Wang
- Cybersecurity Research Institute, Sichuan University, Chengdu 610065, China
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Quan-Hui Liu
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 610054, China
- Compleχ Lab, University of Electronic Science and Technology of China, Chengdu 610054, China
- College of Computer Science, Sichuan University, Chengdu 610065, China
| | - Junhao Liang
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
| | - Yanqing Hu
- School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, China
- Southern Marine Science and Engineering Guangdong Laboratory, Zhuhai, 519082, China
| | - Tao Zhou
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 610054, China
- Compleχ Lab, University of Electronic Science and Technology of China, Chengdu 610054, China
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18
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Iacopini I, Petri G, Barrat A, Latora V. Simplicial models of social contagion. Nat Commun 2019; 10:2485. [PMID: 31171784 PMCID: PMC6554271 DOI: 10.1038/s41467-019-10431-6] [Citation(s) in RCA: 134] [Impact Index Per Article: 26.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2018] [Accepted: 05/03/2019] [Indexed: 11/24/2022] Open
Abstract
Complex networks have been successfully used to describe the spread of diseases in populations of interacting individuals. Conversely, pairwise interactions are often not enough to characterize social contagion processes such as opinion formation or the adoption of novelties, where complex mechanisms of influence and reinforcement are at work. Here we introduce a higher-order model of social contagion in which a social system is represented by a simplicial complex and contagion can occur through interactions in groups of different sizes. Numerical simulations of the model on both empirical and synthetic simplicial complexes highlight the emergence of novel phenomena such as a discontinuous transition induced by higher-order interactions. We show analytically that the transition is discontinuous and that a bistable region appears where healthy and endemic states co-exist. Our results help explain why critical masses are required to initiate social changes and contribute to the understanding of higher-order interactions in complex systems.
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Affiliation(s)
- Iacopo Iacopini
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK
- The Alan Turing Institute, The British Library, London, NW1 2DB, UK
| | - Giovanni Petri
- ISI Foundation, Via Chisola 5, 10126, Turin, Italy
- ISI Global Science Foundation, 33 W 42nd St, New York, NY, 10036, USA
| | - Alain Barrat
- ISI Foundation, Via Chisola 5, 10126, Turin, Italy
- Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, 13009, France
| | - Vito Latora
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK.
- The Alan Turing Institute, The British Library, London, NW1 2DB, UK.
- Dipartimento di Fisica ed Astronomia, Universitá di Catania and INFN, 95123, Catania, Italy.
- Complexity Science Hub Vienna, Josefstädter Strasse 39, Vienna, 1080, Austria.
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19
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Abstract
Acknowledging the significance of awareness diffusion and behavioral response in contagion outbreaks has been regarded as an indispensable prerequisite for a complete understanding of epidemic spreading. Recent studies from the research community have accumulated overwhelming evidence for the incessantly evolving structure of the underlying networks. Thus there is an impelling need to capture the interplay between the epidemic spreading and awareness diffusion on time-varying networks. In this paper, we consider a behavioral model in which susceptible individuals become alert and adopt a preventive behavior under the local risk perception characterized by a decision-making threshold. The impact of awareness diffusion on the epidemic threshold is investigated under the framework of activity-driven network. Results show that the local epidemic situation in risk perception and the duration of preventive effect are crucial for raising the epidemic threshold. The analytical results are corroborated by Monte Carlo simulations.
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20
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Close and ordinary social contacts: How important are they in promoting large-scale contagion? Phys Rev E 2018; 98:052311. [PMCID: PMC7217557 DOI: 10.1103/physreve.98.052311] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
An outstanding problem of interdisciplinary interest is to understand quantitatively the role of social contacts in contagion dynamics. In general, there are two types of contacts: close ones among friends, colleagues and family members, etc., and ordinary contacts from encounters with strangers. Typically, social reinforcement occurs for close contacts. Taking into account both types of contacts, we develop a contact-based model for social contagion. We find that, associated with the spreading dynamics, for random networks there is coexistence of continuous and discontinuous phase transitions, but for heterogeneous networks the transition is continuous. We also find that ordinary contacts play a crucial role in promoting large-scale spreading, and the number of close contacts determines not only the nature of the phase transitions but also the value of the outbreak threshold in random networks. For heterogeneous networks from the real world, the abundance of close contacts affects the epidemic threshold, while its role in facilitating the spreading depends on the adoption threshold assigned to it. We uncover two striking phenomena. First, a strong interplay between ordinary and close contacts is necessary for generating prevalent spreading. In fact, only when there are propagation paths of reasonable length which involve both close and ordinary contacts are large-scale outbreaks of social contagions possible. Second, abundant close contacts in heterogeneous networks promote both outbreak and spreading of the contagion through the transmission channels among the hubs, when both values of the threshold and transmission rate among ordinary contacts are small. We develop a theoretical framework to obtain an analytic understanding of the main findings on random networks, with support from extensive numerical computations. Overall, ordinary contacts facilitate spreading over the entire network, while close contacts determine the way by which outbreaks occur, i.e., through a second- or first-order phase transition. These results provide quantitative insights into how certain social behaviors can emerge and become prevalent, which has potential implications not only to social science but also to economics and political science.
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21
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Milli L, Rossetti G, Pedreschi D, Giannotti F. Active and passive diffusion processes in complex networks. APPLIED NETWORK SCIENCE 2018; 3:42. [PMID: 30460330 PMCID: PMC6214334 DOI: 10.1007/s41109-018-0100-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/09/2018] [Accepted: 09/11/2018] [Indexed: 06/09/2023]
Abstract
Ideas, information, viruses: all of them, with their mechanisms, spread over the complex social information, viruses: all tissues described by our interpersonal relations. Usually, to simulate and understand the unfolding of such complex phenomena are used general mathematical models; these models act agnostically from the object of which they simulate the diffusion, thus considering spreading of virus, ideas and innovations alike. Indeed, such degree of abstraction makes it easier to define a standard set of tools that can be applied to heterogeneous contexts; however, it can also lead to biased, incorrect, simulation outcomes. In this work we introduce the concepts of active and passive diffusion to discriminate the degree in which individuals choice affect the overall spreading of content over a social graph. Moving from the analysis of a well-known passive diffusion schema, the Threshold model (that can be used to model peer-pressure related processes), we introduce two novel approaches whose aim is to provide active and mixed schemas applicable in the context of innovations/ideas diffusion simulation. Our analysis, performed both in synthetic and real-world data, underline that the adoption of exclusively passive/active models leads to conflicting results, thus highlighting the need of mixed approaches to capture the real complexity of the simulated system better.
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Affiliation(s)
- Letizia Milli
- University of Pisa, Largo B. Pontecorvo, 2, Pisa, Italy
- KDD Lab. ISTI-CNR, via G. Moruzzi, 1, Pisa, Italy
| | - Giulio Rossetti
- University of Pisa, Largo B. Pontecorvo, 2, Pisa, Italy
- KDD Lab. ISTI-CNR, via G. Moruzzi, 1, Pisa, Italy
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22
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Min B, San Miguel M. Competition and dual users in complex contagion processes. Sci Rep 2018; 8:14580. [PMID: 30275519 PMCID: PMC6167365 DOI: 10.1038/s41598-018-32643-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2018] [Accepted: 09/04/2018] [Indexed: 11/13/2022] Open
Abstract
We study the competition of two spreading entities, for example innovations, in complex contagion processes in complex networks. We develop an analytical framework and examine the role of dual users, i.e. agents using both technologies. Searching for the spreading transition of the new innovation and the extinction transition of a preexisting one, we identify different phases depending on network mean degree, prevalence of preexisting technology, and thresholds of the contagion process. Competition with the preexisting technology effectively suppresses the spread of the new innovation, but it also allows for phases of coexistence. The existence of dual users largely modifies the transient dynamics creating new phases that promote the spread of a new innovation and extinction of a preexisting one. It enables the global spread of the new innovation even if the old one has the first-mover advantage.
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Affiliation(s)
- Byungjoon Min
- Department of Physics, Chungbuk National University, Cheongju, Chungbuk, 28644, Korea. .,IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122, Palma de Mallorca, Spain.
| | - Maxi San Miguel
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122, Palma de Mallorca, Spain.
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23
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Ruan Z, Wang J, Xuan Q, Fu C, Chen G. Information filtering by smart nodes in random networks. Phys Rev E 2018; 98:022308. [PMID: 30253588 DOI: 10.1103/physreve.98.022308] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2018] [Indexed: 06/08/2023]
Abstract
Diffusion of information in social networks has drawn extensive attention from various scientific communities, with many contagion models proposed to explain related phenomena. In this paper, we present a simple contagion mechanism, in which a node will change its state immediately if it is exposed to the diffusive information. By considering two types of nodes (smart and normal) and two kinds of information (true and false), we study analytically and numerically how smart nodes influence the spreading of information, which leads to information filtering. We find that for randomly distributed smart nodes, the spreading dynamics over random networks with Poisson degree distribution and power-law degree distribution (with relatively small cutoffs) can both be described by the same approximate mean-field equation. Increasing the heterogeneity of the network may elicit more deviations, but not much. Moreover, we demonstrate that more smart nodes make the filtering effect on a random network better. Finally, we study the efficacy of different strategies of selecting smart nodes for information filtering.
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Affiliation(s)
- Zhongyuan Ruan
- College of Computer Science, Zhejiang University of Technology, Hangzhou 310023, China
| | - Jinbao Wang
- College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China
| | - Qi Xuan
- College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China
| | - Chenbo Fu
- College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China
| | - Guanrong Chen
- Department of Electronic Engineering, City University of Hong Kong, Hongkong, China
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24
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Min B, San Miguel M. Competing contagion processes: Complex contagion triggered by simple contagion. Sci Rep 2018; 8:10422. [PMID: 29991815 PMCID: PMC6039514 DOI: 10.1038/s41598-018-28615-3] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Accepted: 06/26/2018] [Indexed: 11/08/2022] Open
Abstract
Empirical evidence reveals that contagion processes often occur with competition of simple and complex contagion, meaning that while some agents follow simple contagion, others follow complex contagion. Simple contagion refers to spreading processes induced by a single exposure to a contagious entity while complex contagion demands multiple exposures for transmission. Inspired by this observation, we propose a model of contagion dynamics with a transmission probability that initiates a process of complex contagion. With this probability nodes subject to simple contagion get adopted and trigger a process of complex contagion. We obtain a phase diagram in the parameter space of the transmission probability and the fraction of nodes subject to complex contagion. Our contagion model exhibits a rich variety of phase transitions such as continuous, discontinuous, and hybrid phase transitions, criticality, tricriticality, and double transitions. In particular, we find a double phase transition showing a continuous transition and a following discontinuous transition in the density of adopted nodes with respect to the transmission probability. We show that the double transition occurs with an intermediate phase in which nodes following simple contagion become adopted but nodes with complex contagion remain susceptible.
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Affiliation(s)
- Byungjoon Min
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122, Palma de Mallorca, Spain.
- Department of Physics, Chungbuk National University, Cheongju, Chungbuk, 28644, Korea.
| | - Maxi San Miguel
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122, Palma de Mallorca, Spain.
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25
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Liu QH, Lü FM, Zhang Q, Tang M, Zhou T. Impacts of opinion leaders on social contagions. CHAOS (WOODBURY, N.Y.) 2018; 28:053103. [PMID: 29857688 DOI: 10.1063/1.5017515] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Opinion leaders are ubiquitous in both online and offline social networks, but the impacts of opinion leaders on social behavior contagions are still not fully understood, especially by using a mathematical model. Here, we generalize the classical Watts threshold model and address the influences of the opinion leaders, where an individual adopts a new behavior if one of his/her opinion leaders adopts the behavior. First, we choose the opinion leaders randomly from all individuals in the network and find that the impacts of opinion leaders make other individuals adopt the behavior more easily. Specifically, the existence of opinion leaders reduces the lowest mean degree of the network required for the global behavior adoption and increases the highest mean degree of the network that the global behavior adoption can occur. Besides, the introduction of opinion leaders accelerates the behavior adoption but does not change the adoption order of individuals. The developed theoretical predictions agree with the simulation results. Second, we randomly choose the opinion leaders from the top h% of the highest degree individuals and find an optimal h% for the network with the lowest mean degree that the global behavior adoption can occur. Meanwhile, the influences of opinion leaders on accelerating the adoption of behaviors become less significant and can even be ignored when reducing the value of h%.
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Affiliation(s)
- Quan-Hui Liu
- Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Feng-Mao Lü
- Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Qian Zhang
- Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, Massachusetts 02115, USA
| | - Ming Tang
- Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Tao Zhou
- Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
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26
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Riedl C, Bjelland J, Canright G, Iqbal A, Engø-Monsen K, Qureshi T, Sundsøy PR, Lazer D. Product diffusion through on-demand information-seeking behaviour. J R Soc Interface 2018; 15:rsif.2017.0751. [PMID: 29467257 PMCID: PMC5832727 DOI: 10.1098/rsif.2017.0751] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2017] [Accepted: 01/29/2018] [Indexed: 11/24/2022] Open
Abstract
Most models of product adoption predict S-shaped adoption curves. Here we report results from two country-scale experiments in which we find linear adoption curves. We show evidence that the observed linear pattern is the result of active information-seeking behaviour: individuals actively pulling information from several central sources facilitated by modern Internet searches. Thus, a constant baseline rate of interest sustains product diffusion, resulting in a linear diffusion process instead of the S-shaped curve of adoption predicted by many diffusion models. The main experiment seeded 70 000 (48 000 in Experiment 2) unique voucher codes for the same product with randomly sampled nodes in a social network of approximately 43 million individuals with about 567 million ties. We find that the experiment reached over 800 000 individuals with 80% of adopters adopting the same product—a winner-take-all dynamic consistent with search engine driven rankings that would not have emerged had the products spread only through a network of social contacts. We provide evidence for (and characterization of) this diffusion process driven by active information-seeking behaviour through analyses investigating (a) patterns of geographical spreading; (b) the branching process; and (c) diffusion heterogeneity. Using data on adopters' geolocation we show that social spreading is highly localized, while on-demand diffusion is geographically independent. We also show that cascades started by individuals who actively pull information from central sources are more effective at spreading the product among their peers.
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Affiliation(s)
- Christoph Riedl
- Northeastern University, Boston, MA, USA .,Harvard University, Cambridge, MA, USA
| | | | | | | | | | | | | | - David Lazer
- Northeastern University, Boston, MA, USA.,Harvard University, Cambridge, MA, USA
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27
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Abstract
Weighted networks capture the structure of complex systems where interaction strength is meaningful. This information is essential to a large number of processes, such as threshold dynamics, where link weights reflect the amount of influence that neighbours have in determining a node's behaviour. Despite describing numerous cascading phenomena, such as neural firing or social contagion, the modelling of threshold dynamics on weighted networks has been largely overlooked. We fill this gap by studying a dynamical threshold model over synthetic and real weighted networks with numerical and analytical tools. We show that the time of cascade emergence depends non-monotonously on weight heterogeneities, which accelerate or decelerate the dynamics, and lead to non-trivial parameter spaces for various networks and weight distributions. Our methodology applies to arbitrary binary state processes and link properties, and may prove instrumental in understanding the role of edge heterogeneities in various natural and social phenomena.
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28
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Valdano E, Fiorentin MR, Poletto C, Colizza V. Epidemic Threshold in Continuous-Time Evolving Networks. PHYSICAL REVIEW LETTERS 2018; 120:068302. [PMID: 29481258 PMCID: PMC7219439 DOI: 10.1103/physrevlett.120.068302] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2017] [Revised: 11/20/2017] [Indexed: 05/11/2023]
Abstract
Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold in continuous time through the infection propagator approach. We introduce the weak commutation condition allowing the interpretation of annealed networks, activity-driven networks, and time scale separation into one formalism. Our work provides a coherent connection between discrete and continuous time representations applicable to realistic scenarios.
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Affiliation(s)
- Eugenio Valdano
- INSERM, Sorbonne Université, Institut Pierre Louis d'Epidémiologie et de Santé Publique IPLESP, F75012 Paris, France
| | - Michele Re Fiorentin
- Center for Sustainable Future Technologies, CSFT@PoliTo, Istituto Italiano di Tecnologia, corso Trento 21, 10129 Torino, Italy
| | - Chiara Poletto
- INSERM, Sorbonne Université, Institut Pierre Louis d'Epidémiologie et de Santé Publique IPLESP, F75012 Paris, France
| | - Vittoria Colizza
- INSERM, Sorbonne Université, Institut Pierre Louis d'Epidémiologie et de Santé Publique IPLESP, F75012 Paris, France
- ISI Foundation, 10126 Torino, Italy
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29
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Rossetti G, Milli L, Rinzivillo S, Sîrbu A, Pedreschi D, Giannotti F. NDlib: a python library to model and analyze diffusion processes over complex networks. INTERNATIONAL JOURNAL OF DATA SCIENCE AND ANALYTICS 2017. [DOI: 10.1007/s41060-017-0086-6] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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30
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Abstract
Online social networks have increasing influence on our society, they may play decisive roles in politics and can be crucial for the fate of companies. Such services compete with each other and some may even break down rapidly. Using social network datasets we show the main factors leading to such a dramatic collapse. At early stage mostly the loosely bound users disappear, later collective effects play the main role leading to cascading failures. We present a theory based on a generalised threshold model to explain the findings and show how the collapse time can be estimated in advance using the dynamics of the churning users. Our results shed light to possible mechanisms of instabilities in other competing social processes.
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Affiliation(s)
- János Török
- Center for Network Science, Central European University, Nádor u. 9, H-1051, Budapest, Hungary.
- Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111, Budapest, Hungary.
| | - János Kertész
- Center for Network Science, Central European University, Nádor u. 9, H-1051, Budapest, Hungary
- Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111, Budapest, Hungary
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31
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Ellinas C, Allan N, Johansson A. Dynamics of organizational culture: Individual beliefs vs. social conformity. PLoS One 2017; 12:e0180193. [PMID: 28665960 PMCID: PMC5493361 DOI: 10.1371/journal.pone.0180193] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2017] [Accepted: 06/12/2017] [Indexed: 11/18/2022] Open
Abstract
The complex nature of organizational culture challenges our ability to infer its underlying dynamics from observational studies. Recent computational studies have adopted a distinctly different view, where plausible mechanisms are proposed to describe a wide range of social phenomena, including the onset and evolution of organizational culture. In this spirit, this work introduces an empirically-grounded, agent-based model which relaxes a set of assumptions that describes past work–(a) omittance of an individual’s strive for achieving cognitive coherence; (b) limited integration of important contextual factors—by utilizing networks of beliefs and incorporating social rank into the dynamics. As a result, we illustrate that: (i) an organization may appear to be increasingly coherent in terms of its organizational culture, yet be composed of individuals with reduced levels of coherence; (ii) the components of social conformity—peer-pressure and social rank—are influential at different aggregation levels.
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Affiliation(s)
- Christos Ellinas
- Engineering Mathematics, University of Bristol, Bristol, United Kingdom
- Systemic Consult Ltd, Bradford-on-Avon, United Kingdom
- * E-mail:
| | - Neil Allan
- Systemic Consult Ltd, Bradford-on-Avon, United Kingdom
- Systems IDC, University of Bristol, Bristol, United Kingdom
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32
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Shu P, Gao L, Zhao P, Wang W, Stanley HE. Social contagions on interdependent lattice networks. Sci Rep 2017; 7:44669. [PMID: 28300198 PMCID: PMC5353708 DOI: 10.1038/srep44669] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2016] [Accepted: 02/13/2017] [Indexed: 11/15/2022] Open
Abstract
Although an increasing amount of research is being done on the dynamical processes on interdependent spatial networks, knowledge of how interdependent spatial networks influence the dynamics of social contagion in them is sparse. Here we present a novel non-Markovian social contagion model on interdependent spatial networks composed of two identical two-dimensional lattices. We compare the dynamics of social contagion on networks with different fractions of dependency links and find that the density of final recovered nodes increases as the number of dependency links is increased. We use a finite-size analysis method to identify the type of phase transition in the giant connected components (GCC) of the final adopted nodes and find that as we increase the fraction of dependency links, the phase transition switches from second-order to first-order. In strong interdependent spatial networks with abundant dependency links, increasing the fraction of initial adopted nodes can induce the switch from a first-order to second-order phase transition associated with social contagion dynamics. In networks with a small number of dependency links, the phase transition remains second-order. In addition, both the second-order and first-order phase transition points can be decreased by increasing the fraction of dependency links or the number of initially-adopted nodes.
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Affiliation(s)
- Panpan Shu
- School of Sciences, Xi’an University of Technology, Xi’an, 710054, China
| | - Lei Gao
- Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, 610054, China
| | - Pengcheng Zhao
- School of Physics and Optoelectronic Engineering, Xidian University, Xi’an, 710071, China
| | - Wei Wang
- Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, 610054, China
- Big data research center, University of Electronic Science and Technology of China, Chengdu 610054, China
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts, 02215, USA
| | - H. Eugene Stanley
- Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts, 02215, USA
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33
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Wang P, Zhang LJ, Xu XJ, Xiao G. Heuristic Strategies for Persuader Selection in Contagions on Complex Networks. PLoS One 2017; 12:e0169771. [PMID: 28072847 PMCID: PMC5224984 DOI: 10.1371/journal.pone.0169771] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2016] [Accepted: 12/21/2016] [Indexed: 11/19/2022] Open
Abstract
Individual decision to accept a new idea or product is often driven by both self-adoption and others' persuasion, which has been simulated using a double threshold model [Huang et al., Scientific Reports 6, 23766 (2016)]. We extend the study to consider the case with limited persuasion. That is, a set of individuals is chosen from the population to be equipped with persuasion capabilities, who may succeed in persuading their friends to take the new entity when certain conditions are satisfied. Network node centrality is adopted to characterize each node's influence, based on which three heuristic strategies are applied to pick out persuaders. We compare these strategies for persuader selection on both homogeneous and heterogeneous networks. Two regimes of the underline networks are identified in which the system exhibits distinct behaviors: when networks are sufficiently sparse, selecting persuader nodes in descending order of node centrality achieves the best performance; when networks are sufficiently dense, however, selecting nodes with medium centralities to serve as the persuaders performs the best. Under respective optimal strategies for different types of networks, we further probe which centrality measure is most suitable for persuader selection. It turns out that for the first regime, degree centrality offers the best measure for picking out persuaders from homogeneous networks; while in heterogeneous networks, betweenness centrality takes its place. In the second regime, there is no significant difference caused by centrality measures in persuader selection for homogeneous network; while for heterogeneous networks, closeness centrality offers the best measure.
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Affiliation(s)
- Peng Wang
- College of Sciences, Shanghai University, Shanghai 200444, China
| | - Li-Jie Zhang
- College of Sciences, Shanghai University, Shanghai 200444, China
| | - Xin-Jian Xu
- College of Sciences, Shanghai University, Shanghai 200444, China
- Key Laboratory of Embedded System and Service Computing (Tongji University), Ministry of Education, Shanghai 201804, China
- * E-mail:
| | - Gaoxi Xiao
- School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore
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34
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Czaplicka A, Toral R, San Miguel M. Competition of simple and complex adoption on interdependent networks. Phys Rev E 2016; 94:062301. [PMID: 28085315 DOI: 10.1103/physreve.94.062301] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2016] [Indexed: 11/07/2022]
Abstract
We consider the competition of two mechanisms for adoption processes: a so-called complex threshold dynamics and a simple susceptible-infected-susceptible (SIS) model. Separately, these mechanisms lead, respectively, to first-order and continuous transitions between nonadoption and adoption phases. We consider two interconnected layers. While all nodes on the first layer follow the complex adoption process, all nodes on the second layer follow the simple adoption process. Coupling between the two adoption processes occurs as a result of the inclusion of some additional interconnections between layers. We find that the transition points and also the nature of the transitions are modified in the coupled dynamics. In the complex adoption layer, the critical threshold required for extension of adoption increases with interlayer connectivity whereas in the case of an isolated single network it would decrease with average connectivity. In addition, the transition can become continuous depending on the detailed interlayer and intralayer connectivities. In the SIS layer, any interlayer connectivity leads to the extension of the adopter phase. Besides, a new transition appears as a sudden drop of the fraction of adopters in the SIS layer. The main numerical findings are described by a mean-field type analytical approach appropriately developed for the threshold-SIS coupled system.
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Affiliation(s)
- Agnieszka Czaplicka
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain
| | - Raul Toral
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain
| | - Maxi San Miguel
- Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain
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Karsai M, Iñiguez G, Kikas R, Kaski K, Kertész J. Local cascades induced global contagion: How heterogeneous thresholds, exogenous effects, and unconcerned behaviour govern online adoption spreading. Sci Rep 2016; 6:27178. [PMID: 27272744 PMCID: PMC4895140 DOI: 10.1038/srep27178] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2016] [Accepted: 05/13/2016] [Indexed: 11/23/2022] Open
Abstract
Adoption of innovations, products or online services is commonly interpreted as a spreading process driven to large extent by social influence and conditioned by the needs and capacities of individuals. To model this process one usually introduces behavioural threshold mechanisms, which can give rise to the evolution of global cascades if the system satisfies a set of conditions. However, these models do not address temporal aspects of the emerging cascades, which in real systems may evolve through various pathways ranging from slow to rapid patterns. Here we fill this gap through the analysis and modelling of product adoption in the world’s largest voice over internet service, the social network of Skype. We provide empirical evidence about the heterogeneous distribution of fractional behavioural thresholds, which appears to be independent of the degree of adopting egos. We show that the structure of real-world adoption clusters is radically different from previous theoretical expectations, since vulnerable adoptions—induced by a single adopting neighbour—appear to be important only locally, while spontaneous adopters arriving at a constant rate and the involvement of unconcerned individuals govern the global emergence of social spreading.
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Affiliation(s)
- Márton Karsai
- Univ de Lyon, ENS de Lyon, INRIA, CNRS, UMR 5668, IXXI, 69364 Lyon, France
| | - Gerardo Iñiguez
- Department of Computer Science, School of Science, Aalto University, 00076, Finland.,Centro de Investigación y Docencia Económicas, CONACYT, 01210 México D.F., Mexico
| | - Riivo Kikas
- Institute of Computer Science, University of Tartu, 50409 Tartu, Estonia.,Software Technology and Applications Competence Center (STACC), 51003 Tartu, Estonia
| | - Kimmo Kaski
- Department of Computer Science, School of Science, Aalto University, 00076, Finland
| | - János Kertész
- Center for Network Science, Central European University, 1051 Budapest, Hungary.,Institute of Physics, Budapest University of Technology and Economics, 1111 Budapest, Hungary
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Abstract
The threshold model has been widely adopted as a classic model for studying contagion processes on social networks. We consider asymmetric individual interactions in social networks and introduce a persuasion mechanism into the threshold model. Specifically, we study a combination of adoption and persuasion in cascading processes on complex networks. It is found that with the introduction of the persuasion mechanism, the system may become more vulnerable to global cascades, and the effects of persuasion tend to be more significant in heterogeneous networks than those in homogeneous networks: a comparison between heterogeneous and homogeneous networks shows that under weak persuasion, heterogeneous networks tend to be more robust against random shocks than homogeneous networks; whereas under strong persuasion, homogeneous networks are more stable. Finally, we study the effects of adoption and persuasion threshold heterogeneity on systemic stability. Though both heterogeneities give rise to global cascades, the adoption heterogeneity has an overwhelmingly stronger impact than the persuasion heterogeneity when the network connectivity is sufficiently dense.
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