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Wang X, Li W, Liu L, Pei S, Tang S, Zheng Z. Promoting information diffusion through interlayer recovery processes in multiplex networks. Phys Rev E 2018; 96:032304. [PMID: 29346939 DOI: 10.1103/physreve.96.032304] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2017] [Indexed: 11/07/2022]
Abstract
For information diffusion in multiplex networks, the effect of interlayer contagion on spreading dynamics has been explored in different settings. Nevertheless, the impact of interlayer recovery processes, i.e., the transition of nodes to stiflers in all layers after they become stiflers in any layer, still remains unclear. In this paper, we propose a modified ignorant-spreader-stifler model of rumor spreading equipped with an interlayer recovery mechanism. We find that the information diffusion can be effectively promoted for a range of interlayer recovery rates. By combining the mean-field approximation and the Markov chain approach, we derive the evolution equations of the diffusion process in two-layer homogeneous multiplex networks. The optimal interlayer recovery rate that achieves the maximal enhancement can be calculated by solving the equations numerically. In addition, we find that the promoting effect on a certain layer can be strengthened if information spreads more extensively within the counterpart layer. When applying the model to two-layer scale-free multiplex networks, with or without degree correlation, similar promoting effect is also observed in simulations. Our work indicates that the interlayer recovery process is beneficial to information diffusion in multiplex networks, which may have implications for designing efficient spreading strategies.
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Affiliation(s)
- Xin Wang
- LMIB, BDBC and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
| | - Weihua Li
- LMIB, BDBC and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
| | - Longzhao Liu
- LMIB, BDBC and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
| | - Sen Pei
- Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York 10032, USA
| | - Shaoting Tang
- LMIB, BDBC and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
| | - Zhiming Zheng
- LMIB, BDBC and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
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Wang W, Tang M, Eugene Stanley H, Braunstein LA. Unification of theoretical approaches for epidemic spreading on complex networks. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:036603. [PMID: 28176679 DOI: 10.1088/1361-6633/aa5398] [Citation(s) in RCA: 100] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical message-passing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks.
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Affiliation(s)
- Wei Wang
- Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, People's Republic of China. Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 610054, People's Republic of China. Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, United States of America
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Viles W, Ginestet CE, Tang A, Kramer MA, Kolaczyk ED. Percolation under noise: Detecting explosive percolation using the second-largest component. Phys Rev E 2016; 93:052301. [PMID: 27300904 DOI: 10.1103/physreve.93.052301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2015] [Indexed: 11/07/2022]
Abstract
We consider the problem of distinguishing between different rates of percolation under noise. A statistical model of percolation is constructed allowing for the birth and death of edges as well as the presence of noise in the observations. This graph-valued stochastic process is composed of a latent and an observed nonstationary process, where the observed graph process is corrupted by type-I and type-II errors. This produces a hidden Markov graph model. We show that for certain choices of parameters controlling the noise, the classical (Erdős-Rényi) percolation is visually indistinguishable from a more rapid form of percolation. In this setting, we compare two different criteria for discriminating between these two percolation models, based on the interquartile range (IQR) of the first component's size, and on the maximal size of the second-largest component. We show through data simulations that this second criterion outperforms the IQR of the first component's size, in terms of discriminatory power. The maximal size of the second component therefore provides a useful statistic for distinguishing between different rates of percolation, under physically motivated conditions for the birth and death of edges, and under noise. The potential application of the proposed criteria for the detection of clinically relevant percolation in the context of applied neuroscience is also discussed.
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Affiliation(s)
- Wes Viles
- Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA
| | - Cedric E Ginestet
- Department of Biostatistics, Institute of Psychiatry, Psychology and Neuroscience, King's College, London, United Kingdom
| | - Ariana Tang
- Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA
| | - Mark A Kramer
- Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA
| | - Eric D Kolaczyk
- Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215, USA
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Breaking of the site-bond percolation universality in networks. Nat Commun 2015; 6:10196. [PMID: 26667155 PMCID: PMC4682156 DOI: 10.1038/ncomms10196] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2015] [Accepted: 11/15/2015] [Indexed: 11/30/2022] Open
Abstract
The stochastic addition of either vertices or connections in a network leads to the observation of the percolation transition, a structural change with the appearance of a connected component encompassing a finite fraction of the system. Percolation has always been regarded as a substrate-dependent but model-independent process, in the sense that the critical exponents of the transition are determined by the geometry of the system, but they are identical for the bond and site percolation models. Here, we report a violation of such assumption. We provide analytical and numerical evidence of a difference in the values of the critical exponents between the bond and site percolation models in networks with null percolation thresholds, such as scale-free graphs with diverging second moment of the degree distribution. We discuss possible implications of our results in real networks, and provide additional insights on the anomalous nature of the percolation transition with null threshold. The percolation transition has been regarded as model-independent, namely determined by the geometry of a system but otherwise identical for bond or site percolation models. Here, the authors show the violation of this assumption both analytically and numerically for networks with null percolation thresholds.
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Li W, Tang S, Fang W, Guo Q, Zhang X, Zheng Z. How multiple social networks affect user awareness: The information diffusion process in multiplex networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042810. [PMID: 26565292 DOI: 10.1103/physreve.92.042810] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2015] [Indexed: 05/20/2023]
Abstract
The information diffusion process in single complex networks has been extensively studied, especially for modeling the spreading activities in online social networks. However, individuals usually use multiple social networks at the same time, and can share the information they have learned from one social network to another. This phenomenon gives rise to a new diffusion process on multiplex networks with more than one network layer. In this paper we account for this multiplex network spreading by proposing a model of information diffusion in two-layer multiplex networks. We develop a theoretical framework using bond percolation and cascading failure to describe the intralayer and interlayer diffusion. This allows us to obtain analytical solutions for the fraction of informed individuals as a function of transmissibility T and the interlayer transmission rate θ. Simulation results show that interaction between layers can greatly enhance the information diffusion process. And explosive diffusion can occur even if the transmissibility of the focal layer is under the critical threshold, due to interlayer transmission.
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Affiliation(s)
- Weihua Li
- School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
- Key Laboratory of Mathematics Informatics Behavioral Semantics (LMIB), Ministry of Education, China
| | - Shaoting Tang
- School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
- Key Laboratory of Mathematics Informatics Behavioral Semantics (LMIB), Ministry of Education, China
| | - Wenyi Fang
- Key Laboratory of Mathematics Informatics Behavioral Semantics (LMIB), Ministry of Education, China
- School of Mathematical Sciences, Peking University, Beijing 100871, China
| | - Quantong Guo
- School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
- Key Laboratory of Mathematics Informatics Behavioral Semantics (LMIB), Ministry of Education, China
| | - Xiao Zhang
- School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
- Key Laboratory of Mathematics Informatics Behavioral Semantics (LMIB), Ministry of Education, China
| | - Zhiming Zheng
- School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
- Key Laboratory of Mathematics Informatics Behavioral Semantics (LMIB), Ministry of Education, China
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Buono C, Vazquez F, Macri PA, Braunstein LA. Slow epidemic extinction in populations with heterogeneous infection rates. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022813. [PMID: 24032889 DOI: 10.1103/physreve.88.022813] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2012] [Indexed: 06/02/2023]
Abstract
We explore how heterogeneity in the intensity of interactions between people affects epidemic spreading. For that, we study the susceptible-infected-susceptible model on a complex network, where a link connecting individuals i and j is endowed with an infection rate β(ij)=λw(ij) proportional to the intensity of their contact w(ij), with a distribution P(w(ij)) taken from face-to-face experiments analyzed in Cattuto et al. [PLoS ONE 5, e11596 (2010)]. We find an extremely slow decay of the fraction of infected individuals, for a wide range of the control parameter λ. Using a distribution of width a we identify two large regions in the a-λ space with anomalous behaviors, which are reminiscent of rare region effects (Griffiths phases) found in models with quenched disorder. We show that the slow approach to extinction is caused by isolated small groups of highly interacting individuals, which keep epidemics alive for very long times. A mean-field approximation and a percolation approach capture with very good accuracy the absorbing-active transition line for weak (small a) and strong (large a) disorder, respectively.
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Affiliation(s)
- C Buono
- Instituto de Investigaciones Físicas de Mar del Plata UNMdP-CONICET and Departamento de Física FCEyN, Universidad Nacional de Mar del Plata, Funes 3350 (7600) Mar del Plata, Argentina
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Valdez LD, Macri PA, Braunstein LA. Intermittent social distancing strategy for epidemic control. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:036108. [PMID: 22587150 DOI: 10.1103/physreve.85.036108] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2011] [Indexed: 05/22/2023]
Abstract
We study the critical effect of an intermittent social distancing strategy on the propagation of epidemics in adaptive complex networks. We characterize the effect of our strategy in the framework of the susceptible-infected-recovered model. In our model, based on local information, a susceptible individual interrupts the contact with an infected individual with a probability σ and restores it after a fixed time t(b). We find that, depending on the network topology, in our social distancing strategy there exists a cutoff threshold σ(c) beyond which the epidemic phase disappears. Our results are supported by a theoretical framework and extensive simulations of the model. Furthermore we show that this strategy is very efficient because it leads to a "susceptible herd behavior" that protects a large fraction of susceptible individuals. We explain our results using percolation arguments.
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Affiliation(s)
- L D Valdez
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR)-Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata-CONICET, Funes 3350, (7600) Mar del Plata, Argentina
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Lagorio C, Dickison M, Vazquez F, Braunstein LA, Macri PA, Migueles MV, Havlin S, Stanley HE. Quarantine-generated phase transition in epidemic spreading. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:026102. [PMID: 21405884 DOI: 10.1103/physreve.83.026102] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2010] [Indexed: 05/04/2023]
Abstract
We study the critical effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered model in the presence of quarantine, where susceptible individuals protect themselves by disconnecting their links to infected neighbors with probability w and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by an analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold w(c) separating a phase (w<w(c)) where the disease reaches a large fraction of the population from a phase (w≥w(c)) where the disease does not spread out. We find that in our model the topology of the network strongly affects the size of the propagation and that w(c) increases with the mean degree and heterogeneity of the network. We also find that w(c) is reduced if we perform a preferential rewiring, in which the rewiring probability is proportional to the degree of infected nodes.
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Affiliation(s)
- C Lagorio
- Departamento de Física, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata-CONICET, Funes 3350, 7600 Mar del Plata, Argentina
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Radicchi F, Fortunato S. Explosive percolation in scale-free networks. PHYSICAL REVIEW LETTERS 2009; 103:168701. [PMID: 19905730 DOI: 10.1103/physrevlett.103.168701] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2009] [Revised: 09/17/2009] [Indexed: 05/28/2023]
Abstract
We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced in order to produce a scale-free graph with given exponent lambda for the degree distribution, but the choice of each new link depends on the mass of the clusters that this link will merge. Networks constructed via this biased procedure show a percolation transition which strongly differs from the one observed in standard percolation, where links are introduced just randomly. The different growth process leads to a phase transition with a nonvanishing percolation threshold already for lambda>lambda(c) approximately 2.2. More interestingly, the transition is continuous when lambda<or=3 but becomes discontinuous when lambda>3. This may have important consequences for both the structure of networks and for the dynamics of processes taking place on them.
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Affiliation(s)
- Filippo Radicchi
- Complex Networks and Systems Group, ISI Foundation, Torino, Italy
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Kownacki JP. Site percolation on planar Phi(3) random graphs. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:021121. [PMID: 18352001 DOI: 10.1103/physreve.77.021121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2007] [Revised: 12/17/2007] [Indexed: 05/26/2023]
Abstract
In this paper, site percolation on random Phi(3) planar graphs is studied by Monte Carlo numerical techniques. The method consists in randomly removing a fraction q = 1-p of vertices from graphs generated by Monte Carlo simulations, where p is the occupation probability. The resulting graphs are made of clusters of occupied sites. By measuring several properties of their distribution, it is shown that percolation occurs for an occupation probability above a percolation threshold p(c) = 0.7360(5) . Moreover, critical exponents are compatible with those analytically known for bond percolation.
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Affiliation(s)
- J-P Kownacki
- Laboratoire de Physique Théorique et Modélisation, CNRS-Université de Cergy-Pontoise-UMR8089, Cergy-Pontoise Cedex, France.
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Ramasco JJ, Gonçalves B. Transport on weighted networks: When the correlations are independent of the degree. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:066106. [PMID: 18233897 DOI: 10.1103/physreve.76.066106] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2007] [Revised: 09/22/2007] [Indexed: 05/25/2023]
Abstract
Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study nondegree dependent correlations between edge weights, generalizing thus the correlations beyond the degree dependent case. We propose a simple method to introduce weight-weight correlations in topologically uncorrelated graphs. This allows us to test different measures to discriminate between the different correlation types and to quantify their intensity. We also discuss here the effect of weight correlations on the transport properties of the networks, showing that positive correlations dramatically improve transport. Finally, we give two examples of real-world networks (social and transport graphs) in which weight-weight correlations are present.
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Affiliation(s)
- José J Ramasco
- CNLL, ISI Foundation, Viale S. Severo 65, I-10133 Torino, Italy.
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