Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis
Abstract
An adaptive network model using SIS epidemic propagation with link-type dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. A compact pairwise approximation for the dynamic network case is also developed and, for the case of link-type independent rewiring, the outcome of epidemics and changes in network structure are concurrently presented in a single bifurcation diagram. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models.
Cite
@article{arxiv.1410.4953,
title = {Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis},
author = {András Szabó-Solticzky and Luc Berthouze and Istvan Z. Kiss and Péter L. Simon},
journal= {arXiv preprint arXiv:1410.4953},
year = {2014}
}