Stabiility Analysis Of Two Classes Of Computer Virus Propagation Models

In recent years,the prevention and treatment of computer virus have been widely concerned by experts,scholars and people from all walks of life.Meanwhile,it also has become one of the most challenging and difficult problems in the field of internet information security.To understand characteristics and the propagation of computer virus,we establish a computer virus propagation model which can effectively predict and control the propagation of virus,as well as,it is constructive to create a safe and harmonious network environment.The main research results are as follows:Based on the relationship between whether users will install anti-virus software in advance and whether users have strong consciousness of the harm of virus,this thesis has improved a class of piecewise SIRS virus propagation models,which mainly studied the stability of two kinds of equilibria(virus-free equilibrium and the virus equilibrium).First,in this model,existing conditions of equilibria were deduced.Second,the local stability of the equilibria was proved through the characteristics of model's Jacobi matrix.And then we further proved the global stability of the equilibria.At last,the simulation results show the equilibria are globally stable.Based on the relationship between antivirus capabilities and the cost of anti-virus software,this thesis has proposed a piecewise SIQRS computer virus propagation model.The stability of two kinds of equilibria of the model was mainly explored.Firstly,basic reproduction number of the system and the existing conditions of equilibria were derived.Secondly,the local stability of the equilibria was proved by Routh-Hurwitz criterion and the center manifold theorem.Next,the global stability of the equilibria was investigated by a Lyapunov function and the LaSalle invariance principle.Then,numerical simulation verified the correctness of the conclusion.Finally,we discussed the influence of parameters of system on the basic reproduction number and put forward three effective defense strategies.