Propagation on networks: an exact alternative perspective

TL;DR

This paper introduces an exact stochastic process for modeling susceptible-infectious dynamics on networks, combining analytical simplicity with computational efficiency, applicable to various systems and network sizes.

Contribution

It presents a novel on-the-fly network generation method and a dual analytical approach for accurate epidemic modeling on finite networks.

Findings

Exact stochastic process models epidemic dynamics efficiently.

Gaussian and branching process approximations are accurate for different outbreak sizes.

Method generalizes to various network-based systems.

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.