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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 2 N -state Markov model and with previously proposed ldquohomogeneousrdquo or ldquolocalrdquo models. The sharp epidemic threshold tau c , which is a consequence of mean field theory, is rigorously shown to be equal to tau c = 1/(lambda max ( A )) , where lambda max ( A ) is the largest eigenvalue-the spectral radius-of the adjacency matrix A . A continued fraction expansion of the steady-state infection probability at node j is presented as well as several upper bounds.
Mieghem et al. (Mon,) studied this question.