Research On Hopf Bifurcation Of Delayed Computer Virus Propagation Model With Quarantine Strategy

In recent years,Internet technology has made considerable achievements,computers have integrated into all fields,and humans' lifestyle has become faster and more flexible.However,these changes also enrich the transmission channels of computer viruses.Since the emergence of computer virus,it has been a major problem in people's production and work,and has caused immeasurable economic losses.In order to effectively administer the spread of computer viruses,common measures include installing anti-virus software and arranging firewalls.But most of these measures are based on known computer viruses,and the speed of their research and development always lags behind the update of computer viruses.To offset the deficiency,it is very necessary to establish an appropriate computer virus propagation model by using the principle of dynamics,reveal the propagation characteristic of computer virus by analyzing the dynamic behavior of relevant models,and put forward scientific and reasonable computer virus control measures on this basis.The aim of this paper is to raise a dynamic model that can better reflect the propagation law of computer virus,and study the propagation regular pattern of computer virus by analyzing its dynamic properties.Based on the existing research work,this paper considers the influence of quarantine strategy and time delay,and establishes two novel time-delay computer virus propagation models with quarantine strategy.The following is a specific statement of the research content:(1)It is very necessary to study the influence of quarantine strategy and the latency characteristics of computer virus on the dissemination process of computer virus.Based on the existing SIRS computer virus propagation model,this paper integrates the quarantine strategy and the latency characteristics of computer virus,and proposes a time-delay SIQRS computer virus propagation model with quarantine strategy.In the research process,not only the equilibrium points of virus-free and virus-existence states are calculated,but also the local asymptotic stability of the two equilibrium points under different time delays is discussed.The existence of Hopf bifurcation of virus-existence equilibrium point and the coefficients of Hopf bifurcation direction and stability are studied.Simulation is the verification of the validity of the theoretical analysis results,and visualization of the research results.Ultimately,in view of the sensitivity analysis of the basic regeneration number of the model,the control measures of computer virus propagation are put forward.(2)Considering the scientificity of hybrid quarantine strategy and the necessity of latent state,the latency state,hybrid quarantine strategy and temporary immune period delay are introduced.Based on the established time-delay SIQRS model,a double time-delay SEIQRS computer virus propagation model with hybrid quarantine strategy is proposed.In the research process,we first calculate the equilibrium points in the two states of virus-free and virus-existence.Later we discuss the local asymptotic stability of the two equilibrium points,and solve the existence of Hopf bifurcation of virus-existence equilibrium point by setting the bifurcation parameters as different combinations of latency delay and temporary immune period delay.Then,we get the direction and stability coefficient of Hopf bifurcation under the certain circumstance.The simulation example not only proves the correctness of the theoretical analysis results,but also visualizes the research results.Finally,by analyzing the sensitivity of the basic regeneration number of the model,some reference suggestions for controlling the spread of computer virus are put forward.The governance of computer virus is an important research content in the current network security field.This study takes the isolation strategy and time delay into account,establishes two new computer virus propagation models,and analyzes the stability of the model under distinct time delay conditions.Then,we put forward some suggestions and countermeasures for the diffusion of computer virus according to the research results: first,update the anti-virus software frequently to improve computer immunity;second,work the software installed in the computer to find the hidden computer virus as early as possible;third,avoid the contact between personal computers and other mobile devices in order to cut off the transmission of computer virus between computers.