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.