Propagation on networks: an exact alternative perspective
  By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of dynamical variables of this birth-death Markov process greatly simplifies analytical calculations. We show how a dual analytical description, treating large scale epidemics with a Gaussian approximations and small outbreaks with a branching process, provides an accurate approximation of the distribution even for rather small networks. The approach also offers important computational advantages and generalizes to a vast class of systems. 
Pierre-Andr\'e No\"el, Antoine Allard, Laurent H\'ebert-Dufresne,   Vincent Marceau and Louis J. Dub\'e
cond-mat.stat-mech cs.SI physics.soc-ph