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Localization and Spreading of Diseases in Complex Networks
A. V. Goltsev, S. N. Dorogovtsev, J. G. Oliveira, J. F. F. Mendes
TL;DR
The paper examines whether SIS diseases must infect a finite fraction of network vertices immediately above the epidemic threshold. Using a spectral approach on unweighted and weighted network models and real-world networks, it shows that localized principal eigenstates can confine disease to finitely many vertices, with hubs and strong-weight edges acting as localization centers.
Problem
The paper addresses the gap between mean-field predictions of finite-fraction infection above threshold and the possibility that disease remains localized on finitely many vertices.
Method
The authors use a spectral approach to the SIS model, analyzing adjacency-matrix eigenstates in unweighted and weighted network models and empirical networks.
Results
Localized principal eigenvectors produce prevalence of order O(1/N) just above λc = 1/Λ1, whereas delocalized eigenvectors produce O(1) prevalence; hubs and strong-weight edges can localize disease.
Takeaways & Limitations
Disease spreading can begin as localization on a finite set of vertices and later undergo a smooth crossover to infection of a finite fraction of vertices.
Abstract
from arXiv · showhide
Using the SIS model on unweighted and weighted networks, we consider the disease localization phenomenon. In contrast to the well-recognized point of view that diseases infect a finite fraction of vertices right above the epidemic threshold, we show that diseases can be localized on a finite number of vertices, where hubs and edges with large weights are centers of localization. Our results follow from the analysis of standard models of networks and empirical data for real-world networks.