  Many real world networks are characterized by adaptive changes in their
topology depending on the dynamic state of their nodes. Here we study epidemic
dynamics in an adaptive network, where susceptibles are able to avoid contact
with infected by rewiring their network connections. We demonstrate that
adaptive rewiring has profound consequences for the emerging network structure,
giving rise to assortative degree correlation and a separation into two loosely
connected sub-compartments. This leads to dynamics such as oscillations,
hysteresis and 1st order transitions. We describe the system in terms of a
simple model using a pair-approximation and present a full local bifurcation
analysis. Our results indicate that the interplay between dynamics and topology
can have important consequences for the spreading of infectious diseases and
related applications.
