Rare regions of the Susceptible Infected Susceptible model on Barabási-Albert networks

Abstract

I extend a previous work to Susceptible-Infected-Susceptible (SIS) models on weighted Barabási-Albert scale-free networks. Numerical evidence is provided that phases with slow, power-law dynamics emerge as the consequence of quenched disorder and tree topologies studied previously with the Contact Process. I compare simulation results with spectral analysis of the networks and show that the quenched mean-field (QMF) approximation provides a reliable, relatively fast method to explore activity clustering. This suggests that QMF can be used for describing rare-region effects due to network inhomogeneities. Finite size study of the QMF shows the expected disappearance of the epidemic threshold ${\lambda }_c$ in the thermodynamic limit and an inverse participation ratio $\sim 0.25$, meaning localization in case of disassortative weight scheme. Contrary, for the multiplicative weights and the unweighted trees this value vanishes in the thermodynamic limit, suggesting only weak rare region effects in agreement with the dynamical simulations. Strong corrections to the mean-field behavior in case of disassortative weights explains the concave shape of the order parameter $\rho (\lambda )$ at the transition point. Application of this method to other models may reveal interesting rare-region effects, Griffiths Phases as the consequence of quenched topological heterogeneities.

arXiv comment6 pages, 4 figures, 1 table, accepted version to appear in PRE

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Cited by in corpus (12)

• Epidemic processes in complex networks
• Slow epidemic extinction in populations with heterogeneous infection rates
• The topology of large Open Connectome networks for the human brain
• Does the brain behave like a (complex) network? I. Dynamics
• Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks
• Critical dynamics on a large human Open Connectome network
• Spectral analysis and slow spreading dynamics on 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
• Localization transition, Lifschitz tails and rare-region effects in network models
• Comparison of mean-field based theoretical analysis methods for SIS model