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

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## 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. 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.

## Keywords

SIS epidemic Pairwise model Dynamic network Oscillation## Mathematics Subject Classification

05C82 60J28 92D30 34C23## Notes

### Acknowledgments

Péter L. Simon acknowledges support from the Hungarian Scientific Research Fund (OTKA) (Grant No. 81403).

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