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Min B, San Miguel M. Threshold Cascade Dynamics in Coevolving Networks. ENTROPY (BASEL, SWITZERLAND) 2023; 25:929. [PMID: 37372273 DOI: 10.3390/e25060929] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Revised: 06/08/2023] [Accepted: 06/09/2023] [Indexed: 06/29/2023]
Abstract
We study the coevolutionary dynamics of network topology and social complex contagion using a threshold cascade model. Our coevolving threshold model incorporates two mechanisms: the threshold mechanism for the spreading of a minority state such as a new opinion, idea, or innovation and the network plasticity, implemented as the rewiring of links to cut the connections between nodes in different states. Using numerical simulations and a mean-field theoretical analysis, we demonstrate that the coevolutionary dynamics can significantly affect the cascade dynamics. The domain of parameters, i.e., the threshold and mean degree, for which global cascades occur shrinks with an increasing network plasticity, indicating that the rewiring process suppresses the onset of global cascades. We also found that during evolution, non-adopting nodes form denser connections, resulting in a wider degree distribution and a non-monotonous dependence of cascades sizes on plasticity.
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Affiliation(s)
- Byungjoon Min
- Department of Physics, Chungbuk National University, Cheongju 28644, Chungbuk, Republic of Korea
- Research Institute for Nanoscale Science and Technology, Chungbuk National University, Cheongju 28644, Chungbuk, Republic of Korea
| | - Maxi San Miguel
- IFISC (CSIC-UIB), Institute for Cross-Disciplinary Physics and Complex Systems, Campus Universitat Illes Balears, E-07122 Palma, Spain
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2
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Abella D, San Miguel M, Ramasco JJ. Aging in binary-state models: The Threshold model for complex contagion. Phys Rev E 2023; 107:024101. [PMID: 36932591 DOI: 10.1103/physreve.107.024101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 12/08/2022] [Indexed: 02/04/2023]
Abstract
We study the non-Markovian effects associated with aging for binary-state dynamics in complex networks. Aging is considered as the property of the agents to be less prone to change their state the longer they have been in the current state, which gives rise to heterogeneous activity patterns. In particular, we analyze aging in the Threshold model, which has been proposed to explain the process of adoption of new technologies. Our analytical approximations give a good description of extensive Monte Carlo simulations in Erdős-Rényi, random-regular and Barabási-Albert networks. While aging does not modify the cascade condition, it slows down the cascade dynamics towards the full-adoption state: the exponential increase of adopters in time from the original model is replaced by a stretched exponential or power law, depending on the aging mechanism. Under several approximations, we give analytical expressions for the cascade condition and for the exponents of the adopters' density growth laws. Beyond random networks, we also describe by Monte Carlo simulations the effects of aging for the Threshold model in a two-dimensional lattice.
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Affiliation(s)
- David Abella
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - Maxi San Miguel
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
| | - José J Ramasco
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
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3
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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: 4] [Impact Index Per Article: 2.0] [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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4
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Diaz-Diaz F, San Miguel M, Meloni S. Echo chambers and information transmission biases in homophilic and heterophilic networks. Sci Rep 2022; 12:9350. [PMID: 35672432 PMCID: PMC9174247 DOI: 10.1038/s41598-022-13343-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 05/23/2022] [Indexed: 12/04/2022] Open
Abstract
We study how information transmission biases arise by the interplay between the structural properties of the network and the dynamics of the information in synthetic scale-free homophilic/heterophilic networks. We provide simple mathematical tools to quantify these biases. Both Simple and Complex Contagion models are insufficient to predict significant biases. In contrast, a Hybrid Contagion model-in which both Simple and Complex Contagion occur-gives rise to three different homophily-dependent biases: emissivity and receptivity biases, and echo chambers. Simulations in an empirical network with high homophily confirm our findings. Our results shed light on the mechanisms that cause inequalities in the visibility of information sources, reduced access to information, and lack of communication among distinct groups.
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Affiliation(s)
- Fernando Diaz-Diaz
- IFISC (UIB-CSIC), Institute for Cross-Disciplinary Physics and Complex Systems, Campus Universitat de les Illes Balears, 07122, Palma de Mallorca, Spain
| | - Maxi San Miguel
- IFISC (UIB-CSIC), Institute for Cross-Disciplinary Physics and Complex Systems, Campus Universitat de les Illes Balears, 07122, Palma de Mallorca, Spain
| | - Sandro Meloni
- IFISC (UIB-CSIC), Institute for Cross-Disciplinary Physics and Complex Systems, Campus Universitat de les Illes Balears, 07122, Palma de Mallorca, Spain.
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5
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Kook J, Choi J, Min B. Double transitions and hysteresis in heterogeneous contagion processes. Phys Rev E 2021; 104:044306. [PMID: 34781441 DOI: 10.1103/physreve.104.044306] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Accepted: 09/22/2021] [Indexed: 11/07/2022]
Abstract
In many real-world contagion phenomena, the number of contacts to spreading entities for adoption varies for different individuals. Therefore, we study a model of contagion dynamics with heterogeneous adoption thresholds. We derive mean-field equations for the fraction of adopted nodes and obtain phase diagrams in terms of the transmission probability and fraction of nodes requiring multiple contacts for adoption. We find a double phase transition exhibiting a continuous transition and a subsequent discontinuous jump in the fraction of adopted nodes because of the heterogeneity in adoption thresholds. Additionally, we observe hysteresis curves in the fraction of adopted nodes owing to adopted nodes in the densely connected core in a network.
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Affiliation(s)
- Joongjae Kook
- Department of Physics, Chungbuk National University, Cheongju, Chungbuk 28644, Korea
| | - Jeehye Choi
- Research Institute for Nanoscale Science and Technology, Chungbuk National University, Cheongju, Chungbuk 28644, Korea
| | - Byungjoon Min
- Department of Physics, Chungbuk National University, Cheongju, Chungbuk 28644, Korea.,Research Institute for Nanoscale Science and Technology, Chungbuk National University, Cheongju, Chungbuk 28644, Korea
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6
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Iacopini I, Schäfer B, Arcaute E, Beck C, Latora V. Multilayer modeling of adoption dynamics in energy demand management. CHAOS (WOODBURY, N.Y.) 2020; 30:013153. [PMID: 32013493 DOI: 10.1063/1.5122313] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2019] [Accepted: 01/14/2020] [Indexed: 06/10/2023]
Abstract
Due to the emergence of new technologies, the whole electricity system is undergoing transformations on a scale and pace never observed before. The decentralization of energy resources and the smart grid have forced utility services to rethink their relationships with customers. Demand response (DR) seeks to adjust the demand for power instead of adjusting the supply. However, DR business models rely on customer participation and can only be effective when large numbers of customers in close geographic vicinity, e.g., connected to the same transformer, opt in. Here, we introduce a model for the dynamics of service adoption on a two-layer multiplex network: the layer of social interactions among customers and the power-grid layer connecting the households. While the adoption process-based on peer-to-peer communication-runs on the social layer, the time-dependent recovery rate of the nodes depends on the states of their neighbors on the power-grid layer, making an infected node surrounded by infectious ones less keen to recover. Numerical simulations of the model on synthetic and real-world networks show that a strong local influence of the customers' actions leads to a discontinuous transition where either none or all the nodes in the network are infected, depending on the infection rate and social pressure to adopt. We find that clusters of early adopters act as points of high local pressure, helping maintaining adopters, and facilitating the eventual adoption of all nodes. This suggests direct marketing strategies on how to efficiently establish and maintain new technologies such as DR schemes.
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Affiliation(s)
- Iacopo Iacopini
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Benjamin Schäfer
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Elsa Arcaute
- Centre for Advanced Spatial Analysis, University College London, London W1T 4TJ, United Kingdom
| | - Christian Beck
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Vito Latora
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
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7
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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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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: 168] [Impact Index Per Article: 33.6] [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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9
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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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10
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Shu P, Liu QH, Wang S, Wang W. Social contagions on interconnected networks of heterogeneous populations. CHAOS (WOODBURY, N.Y.) 2018; 28:113114. [PMID: 30501222 DOI: 10.1063/1.5042677] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2018] [Accepted: 10/26/2018] [Indexed: 06/09/2023]
Abstract
Recently, the dynamics of social contagions ranging from the adoption of a new product to the diffusion of a rumor have attracted more and more attention from researchers. However, the combined effects of individual's heterogenous adoption behavior and the interconnected structure on the social contagions processes have yet to be understood deeply. In this paper, we study theoretically and numerically the social contagions with heterogeneous adoption threshold in interconnected networks. We first develop a generalized edge-based compartmental approach to predict the evolution of social contagion dynamics on interconnected networks. Both the theoretical predictions and numerical results show that the growth of the final recovered fraction with the intralayer propagation rate displays double transitions. When increasing the initial adopted proportion or the adopted threshold, the first transition remains continuous within different dynamic parameters, but the second transition gradually vanishes. When decreasing the interlayer propagation rate, the change in the double transitions mentioned above is also observed. The heterogeneity of degree distribution does not affect the type of first transition, but increasing the heterogeneity of degree distribution results in the type change of the second transition from discontinuous to continuous. The consistency between the theoretical predictions and numerical results confirms the validity of our proposed analytical approach.
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Affiliation(s)
- Panpan Shu
- Xi'an University of Technology, Xi'an 710054, China
| | - Quan-Hui Liu
- Big Data Research Center,University of Electronic Science and Technology of China, Chengdu 610054, China
| | | | - Wei Wang
- Cybersecurity Research Institute, Sichuan University, Chengdu 610065, China
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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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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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Liu QH, Zhong LF, Wang W, Zhou T, Eugene Stanley H. Interactive social contagions and co-infections on complex networks. CHAOS (WOODBURY, N.Y.) 2018; 28:013120. [PMID: 29390629 DOI: 10.1063/1.5010002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
What we are learning about the ubiquitous interactions among multiple social contagion processes on complex networks challenges existing theoretical methods. We propose an interactive social behavior spreading model, in which two behaviors sequentially spread on a complex network, one following the other. Adopting the first behavior has either a synergistic or an inhibiting effect on the spread of the second behavior. We find that the inhibiting effect of the first behavior can cause the continuous phase transition of the second behavior spreading to become discontinuous. This discontinuous phase transition of the second behavior can also become a continuous one when the effect of adopting the first behavior becomes synergistic. This synergy allows the second behavior to be more easily adopted and enlarges the co-existence region of both behaviors. We establish an edge-based compartmental method, and our theoretical predictions match well with the simulation results. Our findings provide helpful insights into better understanding the spread of interactive social behavior in human society.
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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
| | - Lin-Feng Zhong
- Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Wei Wang
- 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
| | - H Eugene Stanley
- Center for Polymer Studies and Department of Physics, Boston, Massachusetts 02215, USA
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Min B, Miguel MS. Fragmentation transitions in a coevolving nonlinear voter model. Sci Rep 2017; 7:12864. [PMID: 28993664 PMCID: PMC5634441 DOI: 10.1038/s41598-017-13047-2] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2017] [Accepted: 09/15/2017] [Indexed: 11/09/2022] Open
Abstract
We study a coevolving nonlinear voter model describing the coupled evolution of the states of the nodes and the network topology. Nonlinearity of the interaction is measured by a parameter q. The network topology changes by rewiring links at a rate p. By analytical and numerical analysis we obtain a phase diagram in p,q parameter space with three different phases: Dynamically active coexistence phase in a single component network, absorbing consensus phase in a single component network, and absorbing phase in a fragmented network. For finite systems the active phase has a lifetime that grows exponentially with system size, at variance with the similar phase for the linear voter model that has a lifetime proportional to system size. We find three transition lines that meet at the point of the fragmentation transition of the linear voter model. A first transition line corresponds to a continuous absorbing transition between the active and fragmented phases. The other two transition lines are discontinuous transitions fundamentally different from the transition of the linear voter model. One is a fragmentation transition between the consensus and fragmented phases, and the other is an absorbing transition in a single component network between the active and consensus phases.
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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, Spain.
| | - Maxi San Miguel
- IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, E-07122, Palma, Spain.
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15
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Artime O, Fernández-Gracia J, Ramasco JJ, San Miguel M. Joint effect of ageing and multilayer structure prevents ordering in the voter model. Sci Rep 2017; 7:7166. [PMID: 28769089 PMCID: PMC5541013 DOI: 10.1038/s41598-017-07031-z] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2017] [Accepted: 06/20/2017] [Indexed: 11/08/2022] Open
Abstract
The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for catalysis and species competition. Inspired by the temporal inhomogeneities found in human interactions, one can introduce ageing in the agents: the probability to update their state decreases with the time elapsed since the last change. This modified dynamics induces an approach to consensus via coarsening in single-layer complex networks. In this work, we investigate how a multilayer structure affects the dynamics of the ageing voter model. The system is studied as a function of the fraction of nodes sharing states across layers (multiplexity parameter q). We find that the dynamics of the system suffers a notable change at an intermediate value q*. Above it, the voter model always orders to an absorbing configuration. While below it a fraction of the realizations falls into dynamical traps associated to a spontaneous symmetry breaking. In this latter case, the majority opinion in the different layers takes opposite signs and the arrival at the absorbing state is indefinitely delayed due to ageing.
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Affiliation(s)
- Oriol Artime
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122, Palma de Mallorca, Spain.
| | - Juan Fernández-Gracia
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus UIB, 07122, Palma de Mallorca, Spain
| | - José J Ramasco
- 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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Velásquez-Rojas F, Vazquez F. Interacting opinion and disease dynamics in multiplex networks: Discontinuous phase transition and nonmonotonic consensus times. Phys Rev E 2017; 95:052315. [PMID: 28618582 PMCID: PMC7219934 DOI: 10.1103/physreve.95.052315] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2016] [Revised: 03/30/2017] [Indexed: 11/26/2022]
Abstract
Opinion formation and disease spreading are among the most studied dynamical processes on complex networks. In real societies, it is expected that these two processes depend on and affect each other. However, little is known about the effects of opinion dynamics over disease dynamics and vice versa, since most studies treat them separately. In this work we study the dynamics of the voter model for opinion formation intertwined with that of the contact process for disease spreading, in a population of agents that interact via two types of connections, social and contact. These two interacting dynamics take place on two layers of networks, coupled through a fraction q of links present in both networks. The probability that an agent updates its state depends on both the opinion and disease states of the interacting partner. We find that the opinion dynamics has striking consequences on the statistical properties of disease spreading. The most important is that the smooth (continuous) transition from a healthy to an endemic phase observed in the contact process, as the infection probability increases beyond a threshold, becomes abrupt (discontinuous) in the two-layer system. Therefore, disregarding the effects of social dynamics on epidemics propagation may lead to a misestimation of the real magnitude of the spreading. Also, an endemic-healthy discontinuous transition is found when the coupling q overcomes a threshold value. Furthermore, we show that the disease dynamics delays the opinion consensus, leading to a consensus time that varies nonmonotonically with q in a large range of the model's parameters. A mean-field approach reveals that the coupled dynamics of opinions and disease can be approximately described by the dynamics of the voter model decoupled from that of the contact process, with effective probabilities of opinion and disease transmission.
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Affiliation(s)
- Fátima Velásquez-Rojas
- IFLYSIB, Instituto de Física de Líquidos y Sistemas Biológicos (UNLP-CONICET), 1900 La Plata, Argentina
| | - Federico Vazquez
- IFLYSIB, Instituto de Física de Líquidos y Sistemas Biológicos (UNLP-CONICET), 1900 La Plata, Argentina
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Nicosia V, Skardal PS, Arenas A, Latora V. Collective Phenomena Emerging from the Interactions between Dynamical Processes in Multiplex Networks. PHYSICAL REVIEW LETTERS 2017; 118:138302. [PMID: 28409987 DOI: 10.1103/physrevlett.118.138302] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2016] [Indexed: 05/28/2023]
Abstract
We introduce a framework to intertwine dynamical processes of different nature, each with its own distinct network topology, using a multilayer network approach. As an example of collective phenomena emerging from the interactions of multiple dynamical processes, we study a model where neural dynamics and nutrient transport are bidirectionally coupled in such a way that the allocation of the transport process at one layer depends on the degree of synchronization at the other layer, and vice versa. We show numerically, and we prove analytically, that the multilayer coupling induces a spontaneous explosive synchronization and a heterogeneous distribution of allocations, otherwise not present in the two systems considered separately. Our framework can find application to other cases where two or more dynamical processes such as synchronization, opinion formation, information diffusion, or disease spreading, are interacting with each other.
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Affiliation(s)
- Vincenzo Nicosia
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | | | - Alex Arenas
- Department d'Enginyeria Informática i Matemátiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
| | - Vito Latora
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
- Dipartimento di Fisica ed Astronomia, Università di Catania and INFN, I-95123 Catania, Italy
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18
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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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