考虑网络流量的无标度网络病毒免疫策略研究

王亚奇; 蒋国平

doi:10.7498/aps.60.060202

摘要

考虑网络交通流量对病毒传播行为的影响,基于平均场理论研究无标度网络上的病毒免疫策略,提出一种改进的熟人免疫机理.理论分析表明,在考虑网络交通流量影响的情况下,当免疫节点密度较小时,随机免疫几乎不能降低病毒的传播速率,而对网络实施目标免疫则能够有效抑制病毒的传播,并且选择度最大的节点进行免疫与选择介数最大的节点进行免疫的效果基本相同.研究还发现,对于网络全局信息未知的情况,与经典熟人免疫策略相比,所提出的免疫策略能够获得更好的免疫效果.通过数值仿真对理论分析进行了验证.

关键词:

Abstract

In this paper, considering the influence of network traffic flow on the spreading behaviors of epidemics and according to the mean-field theory, we investigate the epidemic immunization strategies in scale-free networks, and propose an improved acquaintance immunization mechanism. Theoretical analysis shows that considering the influence of traffic flow, the random immunization can hardly reduce the spreading velocity of epidemics if the density of vaccinated nodes is small. However, the targeted immunization can sharply depress the epidemic spreading even only a tiny fraction of nodes are vaccinated, and the effects of immunizing the most highly connected nodes and vaccinating the nodes with the largest betweenness are almost the same. We also find that if the network global information is unknown, compared with the classical acquaintance immunization strategy, the strategy proposed in this paper can be used to obtain good immune effect. Numerical simulations confirm the theoretical results.

Keywords:

作者及机构信息

王亚奇¹,
蒋国平²

(1)南京邮电大学控制与智能技术研究中心,南京 210003; (2)南京邮电大学控制与智能技术研究中心,南京 210003;南京邮电大学自动化学院,南京 210003

基金项目: 国家自然科学基金 (批准号:60874091)、江苏省高等学校自然科学基础研究计划 (批准号:08KJD510022)、江苏省"六大人才高峰"计划 (批准号:SJ209006)、南京邮电大学引进人才计划 (批准号:NY209021)和江苏省高等学校研究生科研创新计划 (批准号: CX10B-193Z)资助的课题.

Authors and contacts

Wang Ya-Qi¹,
Jiang Guo-Ping²

(1)Center for Control and Intelligence Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China; (2)Center for Control and Intelligence Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China; College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

参考文献

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[2]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[3]	Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
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[7]	Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A 2004 Phys. Rev. Lett. 92 178701
[8]	Zhou T, Yan G, Wang B H 2005 Phys. Rev. E 71 046141
[9]	Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Wang W X, Zhou T 2007 Phys. Lett. A 364 189
[10]	Kim B J, Jun T, Kim J Y, Choi M Y 2006 Physica A 360 493
[11]	Eubank S, Guclu H, Anil-Kumar V S, Marathe M V, Srinivasan A 2004 Nature 429 180184
[12]	Shi H J, Duan Z S, Chen G R 2008 Physica A 387 2133
[13]	Colizza B, Barrat A, Barthélemy M, Vespignani A 2007 BMC Medicine 5 34
[14]	Krause W, Scholz J, Greiner M 2006 Physica A 361 707
[15]	Meloni S, Arenas A, Moreno Y 2009 Proc. Natl. Acad. Sci. USA 106 16897
[16]	Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 036104
[17]	Cohen R , Havlin S, ben Avraham D 2003 Phys. Rev. Lett. 91 247901
[18]	Bai W J, Zhou T, Wang B H 2007 Physica A 384 656
[19]	Wang Y Q, Jiang G P 2010 J. Syst. Eng. 25 773(in Chinese) [王亚奇、蒋国平 2010 系统工程学报 25 773]
[20]	Bogu M, Krioukov D, Claffy K C 2009 Nat. Phys. 5 74
[21]	Fu X C, Small M, Walker D M, Zhang H F 2008 Phys. Rev. E 77 036113
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[23]	Gómez-Gardenes J, Echenique P, Moreno Y 2006 Euro. Phys. J. B 49 259

施引文献

[1]	Dorogovtsev S N, Goltsev A V, Mendes J F F 2008 Rev. Mod. Phys. 80 1275
[2]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[3]	Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
[4]	May R M, Lloyd A L 2001 Phys. Rev. E 64 066112
[5]	Wang Y, Zheng Z G 2009 Acta Phys. Sin. 58 4421 (in Chinese) [王延、郑志刚 2009 物理学报 58 4421]
[6]	Barabsi A L, Albert R 1999 Science 286 509
[7]	Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A 2004 Phys. Rev. Lett. 92 178701
[8]	Zhou T, Yan G, Wang B H 2005 Phys. Rev. E 71 046141
[9]	Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Wang W X, Zhou T 2007 Phys. Lett. A 364 189
[10]	Kim B J, Jun T, Kim J Y, Choi M Y 2006 Physica A 360 493
[11]	Eubank S, Guclu H, Anil-Kumar V S, Marathe M V, Srinivasan A 2004 Nature 429 180184
[12]	Shi H J, Duan Z S, Chen G R 2008 Physica A 387 2133
[13]	Colizza B, Barrat A, Barthélemy M, Vespignani A 2007 BMC Medicine 5 34
[14]	Krause W, Scholz J, Greiner M 2006 Physica A 361 707
[15]	Meloni S, Arenas A, Moreno Y 2009 Proc. Natl. Acad. Sci. USA 106 16897
[16]	Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 036104
[17]	Cohen R , Havlin S, ben Avraham D 2003 Phys. Rev. Lett. 91 247901
[18]	Bai W J, Zhou T, Wang B H 2007 Physica A 384 656
[19]	Wang Y Q, Jiang G P 2010 J. Syst. Eng. 25 773(in Chinese) [王亚奇、蒋国平 2010 系统工程学报 25 773]
[20]	Bogu M, Krioukov D, Claffy K C 2009 Nat. Phys. 5 74
[21]	Fu X C, Small M, Walker D M, Zhang H F 2008 Phys. Rev. E 77 036113
[22]	Callaway D S, Newman M E J, Strogatz S H, Watts D J 2000 Phys. Rev. Lett. 85 5468
[23]	Gómez-Gardenes J, Echenique P, Moreno Y 2006 Euro. Phys. J. B 49 259

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