Stability And Control Of Computer Virus Propagation Models In Networks

With the increasing penetration of information technology (IT)applications to engineering, business and social activities, the threat ofcomputer viruses has become an increasingly important concern for people.Understand and control the spread and development of computer viruses, andestablish mathematical model of computer virus. Reveal the reasons for theprevalence of the virus through the analysis and simulation of the model, andthen find the method of prevention and control strategies for the virus. It isimportant for people to resist computer viruses, well-maintained networksecurity and information security.The main research results of this paper are as follows:1. The state transition of computer virus propagation in networks,stability analysis and establishing mathematical model of computer virus areconsidered. In order to describe the dynamic characteristic of the virus, aconcept of “equivalent day” is presented. By using “equivalent day”, amathematical model of discrete-time computer virus is established. Thedisease-free equilibrium and the disease equilibrium are first derived from themathematical model. Then the sufficient conditions of stability for thedisease-free equilibrium are obtained by the first Lyapunov method. And thesufficient conditions of stability for the disease equilibrium are given by disctheorem. Simulation results demonstrate the effectiveness of the stabilityconditions.2. Stability analysis with vaccination of computer virus model innetworks is discussed. Firstly, establish mathematical model of computervirus. The disease-free equilibrium and the disease equilibrium are firstderived from the mathematical model. Then the sufficient conditions ofstability for the disease-free equilibrium and disease equilibrium are given.Simulation results demonstrate the effectiveness of the stability conditions. 3. Stability analysis of two-type computer viruses model in networks isdiscussed. Firstly, establish discrete-time mathematical model of computervirus. The disease-free equilibrium and the disease equilibrium are firstderived from the mathematical model. Then the sufficient conditions ofstability for the disease-free equilibrium and disease equilibrium are given.Simulation results demonstrate the effectiveness of the stability conditions.4. Stability analysis of a discrete-time computer SEIQR model innetworks is discussed. Firstly, establish discrete-time mathematical model ofcomputer virus. The disease-free equilibrium and the disease equilibrium arefirst derived from the mathematical model. Then the sufficient conditions ofstability for the disease-free equilibrium and disease equilibrium are given.Simulation results demonstrate the effectiveness of the stability conditions5. Discrete-time mathematical model of logic bomb computer virus withdelay is established by using HIV dynamic model for reference. Thedisease-free equilibrium and the disease equilibrium are first derived from themathematical model. Then the sufficient conditions of stability for thedisease-free equilibrium and disease equilibrium are given. Simulation resultsdemonstrate the effectiveness of the stability conditions.6. Control item is added to discrete-time mathematical model ofcomputer virus. The optimal control law of controlling computer virus usingclassical optimal control law is presented. Simulation results demonstrate theeffectiveness of optimal control law.