The effectiveness of vaccinations on the spread of email-borne computer viruses

Abstract

In the last decade, computer viruses have caused tremendous losses to organizations. New viruses continue to cause havoc, in spite of having better antivirus software. It is thus imperative that we understand what factors significantly influence the spread of viruses. In this paper, we model the networks of users as graphs. For simplicity, we assume that every user works only on their own computer. We assume that nodes in the graph are initially susceptible to infection. Once infected, a node may spread the virus (using perhaps, the inbox or address book) until either the virus is removed and the node is immunized. We assume that an immunized node never gets the same virus again. We study the effect of vaccinations in containing the spread of email-borne computer viruses on some traditional structured interconnection graphs, as well as Internet-like small-world graphs. We test the effectiveness of vaccinations in containing the spread of viruses by looking at the total number of nodes infected for different values of the delay D which is incurred in detecting a virus, developing a vaccine and immunizing each infected node. Our simple user model assumes that a user is likely to open an email attachment (and activate the virus) with probability p and delete it with probability 1 - p. Intuitively, one would expect that the fraction of nodes infected would increase slowly as p is varied or as D is varied. Using simulations, we demonstrate that while this is true for the traditional graphs we used, it does not hold for small-world graphs. Since user networks are known to be small-world graphs, this implies that vaccinations are far less effective on real networks than they would be if the user networks were like traditional interconnection graphs