Spectral analysis and slow spreading dynamics on complex networks

Abstract

The Susceptible-Infected-Susceptible (SIS) model is one of the simplest memoryless system for describing information/epidemic spreading phenomena with competing creation and spontaneous annihilation reactions. The effect of quenched disorder on the dynamical behavior has recently been compared to quenched mean-field (QMF) approximations in scale-free networks. QMF can take into account topological heterogeneity and clustering effects of the activity in the steady state by spectral decomposition analysis of the adjacency matrix. Therefore, it can provide predictions on possible rare-region effects, thus on the occurrence of slow dynamics. I compare QMF results of SIS with simulations on various large dimensional graphs. In particular, I show that for Erd\H os-Rényi graphs this method predicts correctly the epidemic threshold and the rare-region effects. Griffiths Phases emerge if the graph is fragmented or if we apply strong, exponentially suppressing weighting scheme on the edges. The latter model describes the connection time distributions in the face-to-face experiments. In case of generalized Barabási-Albert type of networks with aging connections strong rare-region effects and numerical evidence for Griffiths Phase dynamics are shown.

7 pages, 7 figues, 1 table

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Cited by in corpus (21)

• Epidemic processes in complex networks
• Unification of theoretical approaches for epidemic spreading on complex networks
• Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks
• Heterogeneous pair-approximation for the contact process on complex networks
• Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks
• Sampling methods for the quasistationary regime of epidemic processes on regular and complex networks
• Griffiths phases and localization in hierarchical modular networks
• The topology of large Open Connectome networks for the human brain
• Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks
• Wavelet correlations to reveal multiscale coupling in geophysical systems
• Critical dynamics on a large human Open Connectome network
• An overview of epidemic models with phase transitions to absorbing states running on top of complex networks
• Griffiths phases in infinite-dimensional, non-hierarchical modular networks
• Slow, bursty dynamics as the consequence of quenched network topologies
• Robustness of Griffiths effects in homeostatic connectome models
• Activation thresholds in epidemic spreading with motile infectious agents on scale-free networks
• Localization transition, Lifschitz tails and rare-region effects in network models
• Multistage onset of epidemics in heterogeneous networks
• The emergence of Logarithmic-periodic oscillations in Contact process with the topological disorder
• The Griffiths Phase on Hierarchical Modular Networks with Small-world Edges
• Growth strategy determines network performance