计算机工程

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二部无标度网络上病毒传播模型和免疫策略研究

曾凤琳,温罗生   

  1. (重庆大学数学与统计学院,重庆 401331)
  • 收稿日期:2013-06-27 出版日期:2014-08-15 发布日期:2014-08-15
  • 作者简介:曾凤琳(1988-),女,硕士研究生,主研方向:复杂网络,计算机病毒防治;温罗生,副教授、博士。 
  • 基金项目:
    国家自然科学基金资助项目(51174244)。

Research on Epidemic Spreading Model andImmunization Strategy on Bipartite Scale-free Network

ZENG Feng-lin,WEN Luo-sheng   

  1. (College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China)
  • Received:2013-06-27 Online:2014-08-15 Published:2014-08-15

摘要: 针对计算机网络上的病毒传播问题,提出一种二部无标度网络,其节点分为客户机和服务器两类。在二部无标度网络上应用易感-感染-易感(SIS)传播模型,采用率方程的方法研究二部无标度网络上病毒的状态转移和临界行为,得出客户机感染密度与服务器感染密度的关系式。在SIS模型的基础上利用免疫策略,针对相同的网络拓扑和病毒传播模型,分析比较免疫策略的免疫功能,并给出支持理论结果的数值模拟,结果验证了随机免疫、节点度免疫与相识点免疫策略都具有防御病毒传播的功能,并且防疫能力依次增强。

关键词: 二部无标度网络, 幂律分布, 连接矩阵, 率方程, 病毒传播模型, 免疫策略

Abstract: Aiming at the problem of the epidemic spreading on the computer network,a bipartite scale-free network is proposed in which the nodes are divided into servers and clients.By using Susceptible-Infected-Susceptible(SIS) of the network,it applies rate equation approach to research state transition and critical behavior of epidemic on bipartite scale-free network,and the relation between the infection rates of server-to-client and client-to-server is analyzed.Then using the immunization strategy on the SIS model to analyze the function of the immunization strategy when considering the same topology of the network and spreading model.The numerical simulation is presented to support the analytic results.The result is that all of the stochastic immunization,vertex degree immunization and acquaintance immunization strategy can defense against epidemic spreading,and the power of immunization enhanced in proper sequence.

Key words: bipartite scale-free network, power-law distribution, connectivity matrix, rate equation, epidemic spreading model, immunization strategy

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