含时滞的D-SEIQRS网络蠕虫传播动力学分析

ANALYSIS OF DSEIQRS WORM PROPAGATION DYNAMICS WITH TIME DELAY

  • 摘要: 针对杀毒软件查杀新型病毒所需时间以及节点的不同宕机率,提出一类含时滞的 D-SEIQRS 网络蠕 虫传播动力学模型。基于网络蠕虫的传播阈值 σ, 分析无病平衡点和正平衡点稳定性,并计算出 Hopf 分岔的时 滞临界点;研究三个节点状态转移参数对网络蠕虫病毒传播的影响。仿真结果表明,当 σ< 1 时,无病平衡点局部 渐近稳定;当 σ> 1 时,正平衡点局部渐近稳定;通过增大隔离率系数 Ψ, 降低 S-E 状态节点感染率系数 β并提高 节点免疫率 ρ,可以有效控制蠕虫病毒在网络中的传播。

     

    Abstract: Aimed at the time required for antivirus software to check and kill new viruses and the different downtime rates of nodes, a class of DSEIQRS network worm propagation dynamics model with time delay is proposed. Based on the propagation threshold σ of the network worm, the stability of the diseasefree equilibrium point and the positive equilibrium point was analyzed, and the time delay critical point of the Hopf bifurcation was calculated. The influence of the three node transfer parameters on the propagation of the network worm was given. The simulation results show that when σ<1, the diseasefree equilibrium point is locally asymptotically stable; when σ>1, the positive equilibrium point is locally asymptotically stable. Increasing the isolation rate coefficient, descreasing the SE state node infection rate coefficient ψ and increasing the node immunity rate ρ can effectively control the spread of worms in the network.

     

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