Virus Spread in Networks

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.