  The present paper features results on global survival and extinction of an
infection in a multi-layer network of mobile agents. Expanding on a model first
presented in [CHJW22], we consider an urban environment, represented by
line-segments in the plane, in which agents move according to a random waypoint
model based on a Poisson point process. Whenever two agents are at sufficiently
close proximity for a sufficiently long time the infection can be transmitted
and then propagates into the system according to the same rule starting from a
typical device. Inspired by wireless network architectures, the network is
additionally equipped with a second class of agents that is able to transmit a
patch to neighboring infected agents that in turn can further distribute the
patch, leading to a chase-escape dynamics. We give conditions for parameter
configurations that guarantee existence and absence of global survival as well
as an in-and-out of the survival regime, depending on the speed of the devices.
We also provide complementary results for the setting in which the chase-escape
dynamics is defined as an independent process on the connectivity graph. The
proofs mainly rest on percolation arguments via discretization and multiscale
analysis.
