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 R0 = 1. In order to illustrate
the theoretical findings, we construct a new Nonstandard Finite Difference Scheme
(NSFD) that preserves the bifurcation property at R0 = 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.
