1102.0987 (Pierre-André Noël et al.)

Propagation on networks: an exact alternative perspective    [PDF]

Pierre-André Noël, Antoine Allard, Laurent Hébert-Dufresne, Vincent Marceau, Louis J. Dubé

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.

View original: http://arxiv.org/abs/1102.0987