Noise induced dynamics in adaptive networks with applications to epidemiology

Recent work in modeling the coupling between disease dynamics and dynamic social network geometry has led to the examination of how human interactions force a rewiring of connections in a population. Rewiring of the network may be considered an adaptive response to social forces due to disease spread, which in turn feeds back to the disease dynamics. Such epidemic models, called adaptive networks, have led to new dynamical instabilities along with the creation of multiple attracting states. The co-existence of several attractors is sensitive to internal and external fluctuations, and leads to enhanced stochastic oscillatory outbreaks and disease extinction. The aim of this paper is to explore the bifurcations of adaptive network models in the presence of fluctuations and to review some of the new fluctuation phenomena induced in adaptive networks.