Abstract
A worm spread model concerning impulsive control strategy is proposed and analyzed. We prove that there exists a globally attractive virus-free periodic solution when the vaccination rate is larger thanθ1. Moreover, we show that the system is uniformly persistent if the vaccination rate is less thanθ1. Some numerical simulations are also given to illustrate our main results.
Highlights
Computer virus is a kind of computer program that can replicate itself and spread from one computer to others including viruses, worms, and trojan horses
Corollary 4 implies that the computer virus will disappear if the vaccination rate is less than θ1
Our results indicate that a large pulse vaccination rate will lead to eradication of the worm
Summary
Computer virus is a kind of computer program that can replicate itself and spread from one computer to others including viruses, worms, and trojan horses. Since [1, 2] took the first step towards modeling the spread behavior of worms, much effort has been done in the area of developing a mathematical model for the worms propagation [3–13]. These models provide a reasonable qualitative understanding of the conditions under which viruses spread much faster than others and why. Based on the previous facts, we propose an impulsive system to model the process of periodic installing or updating antivirus software on susceptible computers at fixed time for controlling the spread of worm. A brief conclusion is given, and some future research directions are pointed out
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