Abstract
Computer virus spread model concerning impulsive control strategy is proposed and analyzed. We prove that there exists a globally attractive infection-free periodic solution when the vaccination rate is larger thanθ0. Moreover, we show that the system is uniformly persistent if the vaccination rate is less thanθ1. Some numerical simulations are finally given to illustrate the main results.
Highlights
Computer virus is a kind of computer program that can replicate itself and spread from one computer to others
As hardware and software technology develop and computer networks become an essential tool for daily life, the computer virus starts to be a major threat
The trial on better understanding of the computer virus propagation dynamics is an important matter for improving the safety and reliability in computer systems and networks
Summary
Computer virus is a kind of computer program that can replicate itself and spread from one computer to others. Since 1, 2 took the first step towards modeling the spread behavior of computer virus, much effort has been done in the area of developing a mathematical model for the computer virus propagation 3– 13 These models provide a reasonable qualitative understanding of the conditions under which viruses spread much faster than others. There are two common methods that an antivirus software application uses to detect viruses: using a list of virus signature definitions and using a heuristic algorithm to find viruses based on common behaviors. Based on the above 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 computer virus. A brief conclusion is given and some future research directions are pointed out
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