Investigation of dynamics of a virus–antivirus model in complex network
Investigation of dynamics of a virus–antivirus model in complex network
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DOI：
10.1016/j.physa.2014.11.019
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发表时间：
2015-03
影响因子：
3.3
通讯作者：
Jianguo Ren;Yonghong Xu;Jiming Liu
中科院分区：
文献类型：
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作者：
Jianguo Ren;Yonghong Xu;Jiming Liu
基于互联网的拓扑特性，建立了一种新的计算机病毒-反病毒传播动力学模型。我们从理论上分析了该模型的复杂动力学，发现与已有模型不同，该模型存在两个无病毒平衡点，并且可能存在两个病毒平衡点：一个是反病毒无关的，另一个是反病毒依赖的。此外，通过一个与互联网拓扑结构和模型参数相关的阈值分析了无病毒平衡点的稳定性。证明了当阈值小于等于1时，无病毒平衡点交替全局吸引，从而导致病毒根除，而当阈值大于1时，非病毒病毒平衡点全局渐近稳定，导致病毒扩散，而病毒依赖病毒平衡点也是全局渐近稳定的。文中给出了一些数值算例来说明分析结果。
In this paper, a new model of computer virus–antivirus propagation dynamics based on the topology nature of the Internet is established. We analyze theoretically the complex dynamics of the model and it is found that, unlike the existing models, the model admits two virus-free equilibria and possesses possibly two virus equilibria: one being antivirus-independent and the other being antivirus-dependent. Furthermore, the stability of virus-free equilibria is analyzed via a threshold value associated with the topology of the Internet and the model parameters. It is established that, if the threshold value is less than or equal to the unity, the virus-free equilibria are alternatively globally attractive, resulting in virus eradication, while if the threshold value is greater than unity, the antivirus-independent virus equilibrium is globally asymptotically stable, leading to virus diffusion, while the antivirus-dependent virus equilibrium also is globally asymptotically stable. Some numerical examples are presented to illustrate the analytical results.