08-16-2017, 10:21 PM
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 c, which is a consequence of mean field theory, is rigorously shown to be equal to c = 1 / max (A), where max (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.