Interplay between collective behavior and spreading dynamics on complex networks

Li, Kezan; Ma, Zhongjiun; Jia, Zhen; Small, Michael; Fu, Xinchu

doi:10.1063/1.4766677

Cited by 21 publications

(12 citation statements)

References 18 publications

(29 reference statements)

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“…Without loss of generality, the topological structure of deterministic network G is characterized by WS small-world network 29 or BA network. 30 The WS network is generated with probability 0.1 for rewiring links, where each node is symmetrically connected with its six nearest neighbors in its initial nearest-neighbor network.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Estimating the epidemic threshold on networks by deterministic connections

Small

et al. 2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect than those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.

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Section: Numerical Simulationsmentioning

confidence: 99%

Estimating the epidemic threshold on networks by deterministic connections

Small

et al. 2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In [31], authors considered adaptive mechanism between dynamical synchronization and epidemic spreading behavior on complex networks, in which two models of epidemic synchronization were introduced for the first time to analyze the stability of epidemic synchronization and obtained local and global conditions. Following that, the interplay between collective behavior and spreading dynamics on complex networks was further investigated in [32], where several bidirectional networks models of spreading phenomena were constructed, and found that the collective behavior and spreading behavior are influenced each other. But the models in the above two papers are all based on the heterogeneous mean-field theory.…”

Section: Introductionmentioning

confidence: 99%

Feedback pinning control of collective behaviors aroused by epidemic spread on complex networks

Pan

Feng

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper investigates epidemic control behavioral synchronization for a class of complex networks resulting from spread of epidemic diseases via pinning feedback control strategy. Based on the quenched mean field theory, epidemic control synchronization models with inhibition of contact behavior is constructed, combining with the epidemic transmission system and the complex dynamical network carrying extra controllers. By the properties of convex functions and Gerschgorin theorem, the epidemic threshold of the model is obtained, and the global stability of disease-free equilibrium is analyzed. For individual's infected situation, when epidemic spreads, two types of feedback control strategies depended on the diseases' information are designed: the one only adds controllers to infected individuals, the other adds controllers both to infected and susceptible ones. And by using Lyapunov stability theory, under designed controllers, some criteria that guarantee epidemic control synchronization system achieving behavior synchronization are also derived. Several numerical simulations are performed to show the effectiveness of our theoretical results. As far as we know, this is the first work to address the controlling behavioral synchronization induced by epidemic spreading under the pinning feedback mechanism. It is hopeful that we may have more deeper insight into the essence between disease's spreading and collective behavior controlling in complex dynamical networks.

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“…15,16 Unfortunately, little work is devoted to the study of synchronization during epidemic spread. 8,17 Li et al 8 proposed the models of SIS (susceptible-infected-susceptible) and SIR (susceptible-infected-recovered) epidemic synchronization based on heterogeneous mean-field (HMF) theory and studied the dynamics of SIS epidemic synchronization. Li et al 17 also investigated the interplay between collective behaviors and spreading dynamics on complex networks and analyzed the control problem of spreading behaviors.…”

Section: Introductionmentioning

confidence: 99%

Behavioral synchronization induced by epidemic spread in complex networks

Sun

Lou

Duan

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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During the spread of an epidemic, individuals in realistic networks may exhibit collective behaviors. In order to characterize this kind of phenomenon and explore the correlation between collective behaviors and epidemic spread, in this paper, we construct several mathematical models (including without delay, with a coupling delay, and with double delays) of epidemic synchronization by applying the adaptive feedback motivated by real observations. By using Lyapunov function methods, we obtain the conditions for local and global stability of these epidemic synchronization models. Then, we illustrate that quenched mean-field theory is more accurate than heterogeneous mean-field theory in the prediction of epidemic synchronization. Finally, some numerical simulations are performed to complement our theoretical results, which also reveal some unexpected phenomena, for example, the coupling delay and epidemic delay influence the speed of epidemic synchronization. This work makes further exploration on the relationship between epidemic dynamics and synchronization dynamics, in the hope of being helpful to the study of other dynamical phenomena in the process of epidemic spread.

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Interplay between collective behavior and spreading dynamics on complex networks

Cited by 21 publications

References 18 publications

Estimating the epidemic threshold on networks by deterministic connections

Estimating the epidemic threshold on networks by deterministic connections

Feedback pinning control of collective behaviors aroused by epidemic spread on complex networks

Behavioral synchronization induced by epidemic spread in complex networks

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