The evolution of communication technology and the proliferation of electronic devices have rendered adversaries powerful means for targeted attacks via all sorts of accessible resources. In particular, due to the intrinsic interdependence and ubiquitous connectivity of modern communication systems, adversaries can devise malware that propagates through intermediate hosts to approach the target, to which we refer as transmissive attacks. Inspired by biology, the transmission pattern of such an attack in the digital space much resembles the spread of an epidemic in real life. This article describes transmissive attacks, summarizes the utility of epidemic models in communication systems, and draws connections between transmissive attacks and epidemic models. Simulations, experiments, and ongoing research challenges on transmissive attacks are also addressed.