Chase-escape in dynamic device-to-device networks

Abstract: 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.