  We introduce and analyze models for the propagation of malware in pure D2D
networks given via stationary Cox-Gilbert graphs. Here, the devices form a
Poisson point process with random intensity measure $\lambda\Lambda$, where
$\Lambda$ is stationary and given, for example, by the edge-length measure of a
realization of a Poisson-Voronoi tessellation that represents an urban street
system. We assume that, at initial time, a typical device at the center of the
network carries a malware and starts to infect neighboring devices after random
waiting times. Here we focus on Markovian models, where the waiting times are
exponential random variables, and non-Markovian models, where the waiting times
feature strictly positive minimal and finite maximal waiting times. We present
numerical results for the speed of propagation depending on the system
parameters. In a second step, we introduce and analyze a counter measure for
the malware propagation given by special devices called white knights, which
have the ability, once attacked, to eliminate the malware from infected devices
and turn them into white knights. Based on simulations, we isolate parameter
regimes in which the malware survives or is eliminated, both in the Markovian
and non-Markovian setting.
