Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis

TL;DR

This paper investigates oscillating epidemic patterns in a dynamic network model using stochastic and mean-field analysis, revealing complex behaviors like oscillations alongside steady states, and providing insights into the limitations of mean-field models.

Contribution

It introduces a comprehensive analysis combining bifurcation, stochastic simulation, and a new pairwise approximation for dynamic networks, advancing understanding of epidemic oscillations.

Findings

Oscillations occur alongside disease-free and endemic states.

Fourier analysis characterizes stochastic oscillations.

Bifurcation diagrams link epidemic dynamics with network structure.

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.