Mitigating the Spread of a Virus in the Internet

Virus is a traditional and serious threat of the Internet. The spread of a virus and the containment of the spread can be generalized in an abstraction of a two-side problem in which one side tries to spread the infection as much as possible while the other side tries to detect and limit the spread. Two parameters play an important role: (1) the probability of a successful infection, (2) the probability of a successful detection. The existing studies consider both sides of this problem separately. They either study the spread without detection or study the containment when detection is perfectly accurate. A natural question that arises when attack can be detect but the detection may possibly be inaccurate, is whether it is possible to contain the spread and, if it is, then under what conditions? This paper studies the two-side problem with defense strategies that can be grouped into two main classes, (1) Killing strategies, where a node decides to sacrifice itself and possibly deactivate some of its neighbors, and (2) Cutting strategies, where a node decides to cut or deactivate some communication links. Both classes aim at containing the epidemic by disconnecting infected nodes from healthy ones.