title: Propagation on networks: an exact alternative perspective.
abstract: 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 approximation 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.
authors.affiliation: Département de Physique, de Génie Physique et d'Optique, Université Laval, Québec (QC), Canada.
authors.forename: Pierre-André
authors.initials: PA
authors.lastname: Noël
authors.forename: Antoine
authors.initials: A
authors.lastname: Allard
authors.forename: Laurent
authors.initials: L
authors.lastname: Hébert-Dufresne
authors.forename: Vincent
authors.initials: V
authors.lastname: Marceau
authors.forename: Louis J
authors.initials: LJ
authors.lastname: Dubé
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D013269:Stochastic Processes