Impact of impulsive detoxication on the spread of computer virus

Abstract

We discuss the dynamical properties of a SIRS computer virus propagation model with impulsive detoxication and saturation effect. By the Internet, new antivirus software can be released immediately and take effect quickly after it is running. This leads to the circumstance that many infected computers can be cured in a short time. So impulsive detoxication is a vitally important way for prohibiting the spread of network viruses. The theoretical results show that: (a) the virus-free equilibrium is globally stable when the basic reproduction ratio (BRR) is less than unity, (b) the system is uniformly permanent when BRR exceeds unity, and (c) a supercritical bifurcation occurs when BRR equals unity. Several numerical examples also clearly display the results obtained. Finally, some feasible strategies of eradicating electronic viruses are advised.