  We investigate a model for spatial epidemics explicitly taking into account
bi-directional movements between base and destination locations on individual
mobility networks. We provide a systematic analysis of generic dynamical
features of the model on regular and complex metapopulation network topologies
and show that significant dynamical differences exist to ordinary
reaction-diffusion and effective force of infection models. On a lattice we
calculate an expression for the velocity of the propagating epidemic front and
find that in contrast to the diffusive systems, our model predicts a saturation
of the velocity with increasing traveling rate. Furthermore, we show that a
fully stochastic system exhibits a novel threshold for attack ratio of an
outbreak absent in diffusion and force of infection models. These insights not
only capture natural features of human mobility relevant for the geographical
epidemic spread, they may serve as a starting point for modeling important
dynamical processes in human and animal epidemiology, population ecology,
biology and evolution.
