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 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.

8 pages, 4 figures

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• Large deviations of cascade processes on graphs
• Epidemic fronts in complex networks with metapopulation structure
• High-Accuracy Approximation of Evolutionary Pairwise Games on Complex Networks
• Epidemics on contact networks: a general stochastic approach
• Coexistence of phases and the observability of random graphs
• Epidemics on networks with large initial conditions or changing structure