The spread of computer viruses over a reduced scale-free network

Abstract

Due to the high dimensionality of an epidemic model of computer viruses over a general scale-free network, it is difficult to make a close study of its dynamics. In particular, it is extremely difficult, if not impossible, to prove the global stability of its viral equilibrium, if any. To overcome this difficulty, we suggest to simplify a general scale-free network by partitioning all of its nodes into two classes: higher-degree nodes and lower-degree nodes, and then equating the degrees of all higher-degree nodes and all lower-degree nodes, respectively, yielding a reduced scale-free network. We then propose an epidemic model of computer viruses over a reduced scale-free network. A theoretical analysis reveals that the proposed model is bound to have a globally stable viral equilibrium, implying that any attempt to eradicate network viruses would prove unavailing. As a result, the next best thing we can do is to restrain virus prevalence. Based on an analysis of the impact of different model parameters on virus prevalence, some practicable measures are recommended to contain virus spreading. The work in this paper adequately justifies the idea of reduced scale-free networks.