  From footpaths to flight routes, human mobility networks facilitate the
spread of communicable diseases. Control and elimination efforts depend on
characterizing these networks in terms of connections and flux rates of
individuals between contact nodes. In some cases, transport can be
parameterized with gravity-type models or approximated by a diffusive random
walk. As a alternative, we have isolated intranational commercial air traffic
as a case study for the utility of non-diffusive, heavy-tailed transport
models. We implemented new stochastic simulations of a prototypical
influenza-like infection, focusing on the dense, highly-connected United States
air travel network. We show that mobility on this network can be described
mainly by a power law, in agreement with previous studies. Remarkably, we find
that the global evolution of an outbreak on this network is accurately
reproduced by a two-parameter space-fractional diffusion equation, such that
those parameters are determined by the air travel network.
