Virus Spread in Networks

The influence of the network characteristics on the virus spread is analyzed in a new-the <i>N</i> -intertwined Markov chain-model, whose only approximation lies in the application of mean field theory. The mean field approximation is quantified in detail. The <i>N</i> -intertwined model has been compared with the exact 2<sup>N</sup>-state Markov model and with previously proposed ldquohomogeneousrdquo or ldquolocalrdquo models. The sharp epidemic threshold tau<sub>c</sub> , which is a consequence of mean field theory, is rigorously shown to be equal to tau<sub>c</sub> = 1/(lambda<sub>max</sub>(<i>A</i>)) , where lambda<sub>max</sub>(<i>A</i>) is the largest eigenvalue-the spectral radius-of the adjacency matrix <i>A</i> . A continued fraction expansion of the steady-state infection probability at node <i>j</i> is presented as well as several upper bounds.

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