The spread of a virus and the containment of such spread have been widely studied in the literature. These two problems can be abstracted as a two-players stochastic game in which one side tries to spread the infection to the entire system, while the other side aims to contain the infection to a finite area. Three parameters play a particularly important role: (1) the probability p of successful infection, (2) the topology of the network, and (3) the probability \alpha that a strategy message has priority over the infection.
This paper studies the effect of killing strategies, where a node sacrifices itself and possibly some of its neighbors, to contain the spread of a virus in an infinite grid. Our contribution is threefold: (1) We prove that the simplest killing strategy is equivalent to the problem of site percolation; (2) when killing messages have priority, we prove that there always exists a killing strategy that contains a virus, for any probability 0<=p<1; in contrast, (3) when killing message do not have priority, there is not always a successful killing strategy, and we study the virus propagation for various 0<=\alpha<1.
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