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Virus spread in networks

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Author: Mieghem, P. van · Omic, J. · Kooij, R.E.
Type:article
Date:2009
Institution: TNO Informatie- en Communicatietechnologie
Source:IEEE/ACM Transactions on Networking, 1, 17, 1-14
Identifier: 241329
doi: doi:10.1109/TNET.2008.925623
Keywords: Informatics · Epidemic threshold · Markov theory · Mean field theory · Spectral radius · Virus spread · Markov processes · Mean field theory · Statistical mechanics · Viruses · Adjacency matrices · Continued fraction expansions · Epidemic threshold · In networks · Largest eigenvalue · Markov chains · Markov models · Markov theory · Mean-field approximations · Network characteristics · Spectral radius · Upper bounds · Computer viruses

Abstract

The influence of the network characteristics on the virus spread is analyzed in a new-the N-intertwined Markov chain-model, whose only approximation lies in the application of mean field theory. The mean field approximation is quantified in detail. The N-intertwined model has been compared with the exact 2N-state Markov model and with previously proposed "homogeneous"or "local"models. The sharp epidemic threshold τc, which is a consequence of mean field theory, is rigorously shown to be equal to τc= (λmax (A)), where λmax (A) is the largest eigenvalue-the spectral radius-of the adjacency matrix A.A. A continued fraction expansion of the steady-state infection probability at node j is presented as well as several upper bounds. © 2008 IEEE.