  By generating transient encounters between individuals beyond their immediate
social environment, transport can have a profound impact on the spreading of an
epidemic. In this work, we consider epidemic dynamics in the presence of the
transport process that gives rise to a multiplex network model. In addition to
a static layer, the (multiplex) epidemic network consists of a second dynamic
layer in which any two individuals are connected for the time they occupy the
same site during a random walk they perform on a separate transport network. We
develop a mean-field description of the stochastic network model and study the
influence the transport process has on the epidemic threshold. We show that any
transport process generally lowers the epidemic threshold because of the
additional connections it generates. In contrast, considering also random walks
of fractional order that in some sense are a more realistic model of human
mobility, we find that these non-local transport dynamics raise the epidemic
threshold in comparison to a classical local random walk. We also test our
model on a realistic transport network (the Munich U-Bahn network), and
carefully compare mean-field solutions with stochastic trajectories in a range
of scenarios.
