We study the standard SIS model of epidemic spreading on networks where individuals have a fluctuating number of connections around a preferred degree $\kappa$.
Using very simple rules for forming such preferred degree networks, we find some unusual statistical properties not found in familiar Erd\H{o}s-R\'enyi or scale free networks. Preferred degree networks with adaptive $\kappa$ provide a natural platform to study adaptive contact processes. By letting $\kappa$ depend on the fraction of infected individuals, we model the behavioral changes in response to how the extent of the epidemic is perceived. Specifically, we explore how various simple feedback mechanisms affect transitions between active and absorbing states. For the static case, we find that the infection threshold follows the heterogeneous mean field result $\lambda_{c}=<k>/<k^{2}>$ and the phase diagram matches the predictions of the annealed adjacency matrix (AAM) approach. For the adaptive SIS case we find, surprisingly, that even when the average degree shifts, the epidemic threshold does not change. However, the infection level is substantially altered in the active state. A simple mean field analysis is shown to capture the qualitative and some of the quantitative features of the infection phase diagram.