  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.
