Virus Spread in Networks


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 = 1 / λmax (A), where λmax (A) is the largest eigen value – 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.