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 homogeneous or local 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.