Bifurcation analysis of a computer virus propagation model

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