Bifurcation analysis of a computer virus propagation model

Abstract

We propose a mathematical model for investigating the efficacy of Countermeasure Competing (CMC) strategy which is a method for reducing the effect of computer virus attacks. Using the Centre Manifold Theory, we determine conditions under which a subcritical (backward) bifurcation occurs at Basic Reproduction Number $R_{0}=1$. In order to illustrate the theoretical findings, we construct a new Nonstandard Finite Difference Scheme (NSFD) that preserves the bifurcation property at $R_{0}=1$ among other dynamics of the continuous model. Earlier results given by Chen and Carley [The impact of countermeasure propagation on the prevalence of computer viruses, IEEE Trans. Syst., Man, Cybern. B. Cybern. 2004] show that the CMC strategy is effective when the countermeasure propagation rate is higher than the virus spreading rate. Our results reveal that even if this condition is not met, the CMC strategy may still successfully eradicate computer viruses depending on the extent of its effectiveness.