Qualitative Analysis Of Computer Virus With Two Delays And Optimal Control Model

With the advance of computer hardware technology and communication technology, the number and sort of computer viruses have increased dramatically, which leads to great economic loss and social scare. It's urgent to prevent and control the spread of computer viruses effectively. The study of computer virus is divided into two aspects: the microcosmic aspect and the macroscopic aspect, the former one aims to study the logic structure of computer virus, and to develop program that can detect and remove virus effectively. But the disadvantage of this method is lack of timeliness and prospective,which cannot predict the development trend of computer virus and provide effective protection strategy. In order to control the spread of computer viruses, macroscopic research method began to arouse people's attention.That is to establish a reasonable model of viral transmission, to understand the law of virus' s spread through the model analysis,and then provide effective control and protection. This paper aims to establish and study the dynamic system model of two kinds of computer viruses, and to analyze the dynamic behavior of the model.First of all, in view of the characteristic of the computer virus with no permanent immunity and latency, a SEIRS computer virus model with two delays and saturate incidence is proposed. The existence and stability of the virus-free equilibrium and the viral equilibrium are analyzed. Some sufficient conditions for global attractivity of the equilibrium are also established.Next, we study the problem on the spread of computer virus by establishing an optimal control model with the optimal control strategy. First, we establish a SLBRS optimal control model based on a SLBRS model. Then, we propose the optimal control problem of this model and give the objective functional of it. The existence and uniqueness of the optimal control problem are also proved under some reasonable assumptions. Finally, some numerical simulations are given and the result show that the spread of computer virus can be suppressed effectively by adopting an optimal control strategy.