操作系统病毒时滞传播模型及抑制策略设计

Time-Delay Propagation Model and Suppression Strategy Design of Operating System Virus

为了有效抑制操作系统病毒在网络中的传播,针对操作系统病毒的目标性强和感染时滞等特点,提出了操作系统病毒的时滞传播模型及抑制策略。在经典SIRS模型基础上,考虑操作系统切换和感染阶段时耗因素,引入新的节点状态和感染时滞,构建了操作系统病毒的时滞模型,并给出了系统的平衡点和基本再生数;运用Lyapunov直接法,证明了网络系统在无病毒平衡点处的全局稳定性;根据Hopf分岔理论,计算了网络存在有病毒平衡点时出现分叉的阈值,分析了有病毒平衡点处的Hopf分岔行为;针对感染时滞过高时的振荡现象,设计了相应病毒传播抑制策略,通过微调操作系统切换频率消除振荡现象,在感染节点数稳定后,参照基本再生数重新调整操作系统切换频率,从而彻底消除病毒。理论和仿真结果表明:当基本再生数小于1时,网络能在无病毒平衡点处全局渐进稳定,此时网络可依赖自身免疫能力消除操作系统病毒;当基本再生数大于1且时滞大于对应阈值时,感染节点数存在周期性振荡,此时网络环境难以判定,通过微调操作系统切换频率可消除振荡;当基本再生数大于1且时滞小于对应阈值时,网络在有病毒平衡点处局部渐进稳定,此时网络安全态势明确,可根据基本再生数调整操作切换频率,彻底消除操作系统病毒。

To effectively suppress operating system virus propagation in the network,a time-delay propagation model and the suppression strategy of operating system virus are proposed aiming at the characteristics of operating system virus,such as strong target and delay of infection.Based on the SIRS model,a new state and the infection time delay are introduced.The time-delay model of the operating system virus is constructed.The equilibrium point and the basic regeneration number are given.The global stability of network system at the virus-free equilibrium point is proved by direct Lyapunov method.According to Hopf bifurcation theory,the threshold of bifurcation is calculated,and the Hopf bifurcation behavior is analyzed at the virus equilibrium point.To solve the oscillation in the case of too high infection time delay,the virus propagation suppression strategy is designed.The oscillation can be eliminated by fine-tuning the switching frequency of the operating system.When the number of infected nodes is stable,switching frequency of the operating system is renewed with reference to the basic regeneration number.to eliminate virus completely.The theoretical and simulation results show that when the basic regeneration number is less than 1,the network can be globally asymptotically stable at the virus-free equilibrium point.The network can eliminate the operating system virus relying on its own immunity.When the basic regeneration number is greater than 1 and the time delay is greater than the corresponding threshold,the number of infected nodes has periodic oscillation.It is difficult to determine the network environment at this time.The oscillation can be eliminated by fine-tuning the operating system switching frequency.When the basic regeneration number is greater than 1 and the time delay is less than the corresponding threshold,the network is locally asymptotically stable at the virus equilibrium point,and the network security situation is clear.At this time,the operation switching frequency can be adjusted according to the basic regeneration number to ensure network security.