We feature results on global survival and extinction of an infection in a multi-layer network of mobile agents. Expanding on a model first presented in Cali et al. (2022), 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 able to transmit a patch to neighboring infected agents that in turn can further distribute the patch, leading to 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.

我们展示了多层移动代理网络中感染的全球生存和灭绝的结果。扩展 Cali等人首次提出的模型。（2022），我们考虑由平面中的线段表示的城市环境，其中代理根据基于泊松点过程的随机路径点模型移动。只要两个代理在足够长的时间内足够接近，感染就可以传播，然后根据从典型设备开始的相同规则传播到系统中。受无线网络架构的启发，该网络还配备了第二类代理，能够将补丁传输到邻近的受感染代理，而这些代理又可以进一步分发补丁，从而导致追逐-逃脱的动态。我们给出了参数配置的条件，以保证全局生存的存在和不存在以及生存机制的进出，具体取决于设备的速度。我们还为追逐-逃逸动力学被定义为连接图上的独立过程的设置提供了补充结果。证明主要依赖于通过离散化和多尺度分析进行的渗透论证。