Solving the Dynamic Correlation Problem of the Susceptible-Infected-Susceptible Model on Networks

Cai, Chao-Ran; Wu, Zhi-Xi; Chen, Michael Z. Q.; Holme, Petter; Guan, Jiancheng

doi:10.1103/physrevlett.116.258301

Cited by 82 publications

(56 citation statements)

References 48 publications

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“…Epidemic spreading, one of the most prominent and widely investigated issues, is usually investigated by means of stochastic agent-based models [4]. Despite several advances in the understanding of epidemic models on networks [4][5][6][7][8][9][10][11], it remains target of recent intensive investigations [12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks

2018

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We analyze two alterations of the standard susceptible-infected-susceptible (SIS) dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree. All models have the same epidemic thresholds in mean-field theories but depending on the network properties, simulations yield a dual scenario, in which the epidemic thresholds of the modified SIS models can be either dramatically altered or remain unchanged in comparison with the standard dynamics. For uncorrelated synthetic networks having a power-law degree distribution with exponent γ<5/2, the SIS dynamics are robust exhibiting essentially the same outcomes for all investigated models. A threshold in better agreement with the heterogeneous rather than quenched mean-field theory is observed in the modified dynamics for exponent γ>5/2. Differences are more remarkable for γ>3, where a finite threshold is found in the modified models in contrast with the vanishing threshold of the original one. This duality is elucidated in terms of epidemic lifespan on star graphs. We verify that the activation of the modified SIS models is triggered in the innermost component of the network given by a k-core decomposition for γ<3 while it happens only for γ<5/2 in the standard model. For γ>3, the activation in the modified dynamics is collective involving essentially the whole network while it is triggered by hubs in the standard SIS. The duality also appears in the finite-size scaling of the critical quantities where mean-field behaviors are observed for the modified but not for the original dynamics. Our results feed the discussions about the most proper conceptions of epidemic models to describe real systems and the choices of the most suitable theoretical approaches to deal with these models.

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Section: Introductionmentioning

confidence: 99%

Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks

2018

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“…Another disadvantage is that the pairwise approximation approach usually cannot show an analytical expression of the epidemic threshold, but only a numerical value. Moreover, other approaches were proposed for certain specific dynamics, including the master equations [60] and other generalized ones [61].…”

Section: Theoretical Approachesmentioning

confidence: 99%

Coevolution spreading in complex networks

et al. 2019

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a b s t r a c tThe 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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“…Here, the crucial simplification is to treat the epidemic states of l and its neighbors as mutually independent, which is sometimes referred as neglecting dynamic correlations [59]. The marginal probability I l (t + 1) follows from two independent contributions: (i) The out-flux µI l (t) indicates the transition from the infected to the recovered state.…”

Section: A Individual-based Modelmentioning

confidence: 99%

Contact-Based Model for Epidemic Spreading on Temporal Networks

et al. 2019

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We present a contact-based model to study the spreading of epidemics by means of extending the dynamic message passing approach to temporal networks. The shift in perspective from nodeto edge-centric quantities enables accurate modelling of Markovian susceptible-infected-recovered outbreaks on time-varying trees, i.e., temporal networks with a loop-free underlying topology. On arbitrary graphs, the proposed contact-based model incorporates potential structural and temporal heterogeneities of the underlying contact network and improves analytic estimations with respect to the individual-based (node-centric) approach at a low computational and conceptual cost. Within this new framework, we derive an analytical expression for the epidemic threshold on temporal networks and demonstrate the feasibility of this method on empirical data.

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Solving the Dynamic Correlation Problem of the Susceptible-Infected-Susceptible Model on Networks

Cited by 82 publications

References 48 publications

Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks

Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks

Coevolution spreading in complex networks

Contact-Based Model for Epidemic Spreading on Temporal Networks

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