  The common real-world feature of individuals migrating through a network --
either in real space or online -- significantly complicates understanding of
network processes. Here we show that even though a network may appear static on
average, underlying nodal mobility can dramatically distort outbreak profiles.
Highly nonlinear dynamical regimes emerge in which increasing mobility either
amplifies or suppresses outbreak severity. Predicted profiles mimic recent
outbreaks of real-space contagion (social unrest) and online contagion
(pro-ISIS support). We show that this nodal mobility can be renormalized in a
precise way for a particular class of dynamical networks.
