  We propose a model for epidemic spreading on a finite complex network with a
restriction to at most one contamination per time step. Because of a highly
discrete character of the process, the analysis cannot use the continous
approximation, widely exploited for most of the models. Using discrete approach
we investigate the epidemic threshold and the quasi-stationary distribution.
The main result is a theorem about mixing time for the process, which scales
like logarithm of the network size and which is proportional to the inverse of
the distance from the epidemic threshold. In order to present the model in the
full context, we review modern approach to epidemic spreading modeling based on
complex networks and present necessary information about random networks,
discrete-time Markov chains and their quasi-stationary distributions.
