Metastable Localization of Diseases in Complex Networks

Abstract

We describe the phenomenon of localization in the epidemic SIS model on highly heterogeneous networks in which strongly connected nodes (hubs) play the role of centers of localization. We find that in this model the localized states below the epidemic threshold are metastable. The longevity and scale of the metastable outbreaks do not show a sharp localization transition, instead there is a smooth crossover from localized to delocalized states as we approach the epidemic threshold from below. Analyzing these long-lasting local outbreaks for a random regular graph with a hub, we show how this localization can be detected from the shape of the distribution of the number of infective nodes.

5 pages, 4 figures; Added Appendix

References in corpus (5)

• Critical phenomena in complex networks
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Solving the Dynamic Correlation Problem of the Susceptible-Infected-Susceptible Model on Networks
• Collective versus hub activation of epidemic phases on networks
• Localization transition, Lifschitz tails and rare-region effects in network models

Cited by in corpus (7)

• Optimized evolution of networks for principal eigenvector localization
• Clustering for epidemics on networks: a geometric approach
• Network localization is unalterable by infections in bursts
• Simple quasistationary method for simulations of epidemic processes with localized states
• Rare events in networks with internal and external noise
• Localization of nonbacktracking centrality on dense subgraphs of sparse networks
• Wheel graph strategy for PEV localization of networks