  Disease awareness in epidemiology can be modelled with adaptive contact
networks, where the interplay of disease dynamics and network alteration often
adds new phases to the standard models (Gross et al. 2006, Shaw et al. 2008)
and, in stochastic simulations, lets network topology settle down to a steady
state that can be static (in the frozen phase) or dynamic (in the endemic
phase). We show for the SIS model that, in the endemic phase, this steady state
does not depend on the initial network topology, only on the disease and
rewiring parameters and on the link density of the network, which is conserved.
We give an analytic description of the structure of this co-evolving network of
infection through its steady-state degree distribution.
