On the efficiency of the equation-free closure of statistical moments: Dynamical properties of a stochastic epidemic model on Erdos-Rényi networks

摘要

We show how different explicit statistical moment closures, including the mean field and the Kirkwood approximations as well as an Ursell-type expansion for the moments, compare with the equation-free approach in the case of a stochastic epidemic model evolving on Erds-Rényi networks. For illustration purposes we use a simple, discrete susceptible-infected-recovered stochastic model with a nonlinear recovering probability. For every closure scheme, we derive the corresponding macroscopic evolution equations and we construct the bifurcation diagrams with respect to the probability of infection. Finally, we construct the coarse-grained bifurcation diagram obtained with the equation-free method acting directly on the microscopic simulations, bypassing the derivation of explicit closures. We show that the equation-free approach captures the actual emergent nonlinear behavior and outperforms all the other explicit schemes. © 2012 IOP Publishing Ltd and SISSA Medialab srl.