Beyond Herd Immunity Against Strategic Attackers

Herd immunity, one of the most fundamental concepts in network epidemics, occurs when a large fraction of the population of devices is immune against a virus or malware. The few individuals who have not taken countermeasures against the threat are assumed to have very low chances of infection, as they are indirectly protected by the rest of the devices in the network. Although very fundamental, herd immunity does not account for strategic attackers scanning the network for vulnerable nodes. In face of such attackers, nodes who linger vulnerable in the network become easy targets, compromising cybersecurity. In this paper, we propose an analytical model which allows us to capture the impact of countermeasures against attackers when both endogenous as well as exogenous infections coexist. Using the proposed model, we show that a diverse set of potential attacks produces non-trivial equilibria, some of which go counter to herd immunity; e.g., our model suggests that nodes should adopt countermeasures even when the remainder of the nodes has already decided to do so.