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复杂网络中考虑不完全免疫的病毒传播研究

王亚奇 蒋国平

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复杂网络中考虑不完全免疫的病毒传播研究

王亚奇, 蒋国平

Virus spreading on complex networks with imperfect immunization

Wang Ya-Qi, Jiang Guo-Ping
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  • 复杂网络中不完全免疫包括免疫失败和免疫失效两种情况,本文研究两者同时存在对网络病毒传播行为的影响,基于平均场理论,提出一种新的传播模型.理论分析表明,免疫失败和免疫失效同时存在显著降低了网络的传播临界值,增强了病毒的感染程度.根据传播临界值与免疫节点密度、免疫成功率以及免疫失效率之间的关系,给出有效控制网络病毒传播的策略.通过数值仿真进行验证.
    The imperfect immunization includes immune failure and immune invalidity on complex networks. In this paper, based on mean-field theory, we propose a new susceptible-infected-removed model to study epidemic spreading in networks with both immune failure and immune invalidity. Theoretical analysis shows that the immune failure and immune invalidity can significantly reduce the epidemic threshold and enhance the epidemic prevalence in the networks. According to the relationships between epidemic threshold, immune density of nodes, immune success rate and immune invalid rate, some suggestions on how to effectively control the propagation of epidemics are presented. Numerical simulations have confirmed the theoretical results.
    • 基金项目: 教育部新世纪优秀人才支持计划(批准号:NCET-06-0510)、国家自然科学基金(批准号:60874091)和江苏省"六大人才高峰"高层次人才计划(批准号:SJ209006)资助的课题.
    [1]

    Li X, Wang X F 2006 IEEE Trans. Automatic Control 51 534

    [2]

    Li X, Wang X F 2007 Int. J. Syst. Sci. 38 400

    [3]

    Song Y R, Jiang G P 2009 Acta Phys. Sin. 58 5911 (in Chinese) [宋玉蓉、蒋国平 2009 物理学报 58 5911]

    [4]

    Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Xu W, Zhou T 2007 Phys. Lett. A 386 189

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    Pei W D, Chen Z Q, Yang Z Z 2008 Chin. Phys. B 17 373

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    Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A 2005 J. Theo. Bio. 235 275

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    Zhou T, Liu J G, Bai W J, Chen G R, Wang B H 2006 Phys. Rev. E 74 056109

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    Hayashi Y, Minoura M, Matsukubo J 2004 Phys. Rev. E 69 016112

    [9]

    Huang W, Jiang R, Hu M B, Wu Q S 2009 Chin. Phys. B 18 1306

    [10]

    Zhang H F, Michael S, Fu X C 2009 Commun. Theor. Phys. 52 180

    [11]

    Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200

    [12]

    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]

    [13]

    Watts D J, Strogatz S H 1998 Nature 393 440

    [14]

    Barabsi A L, Albert R 1999 Science 286 509

    [15]

    Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117

    [16]

    Lloyd A L, May R M 2001 Science 292 1316

    [17]

    Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 036104

    [18]

    Guo W P, Li X, Wang X F 2004 Physica A 380 684

    [19]

    Cohen R , Havlin S, ben-Avraham D 2003 Phys. Rev. Lett. 91 247901

    [20]

    Bose T, Trimper S 2009 Phys. Rev. E 79 051903

    [21]

    Gumel A B, McCluskey C C, van den Driessche P 2006 Bull. Math. Biol. 68 2105

    [22]

    Yip P, Watson R, Chen Q Z 2007 Statist. Med. 26 4475

    [23]

    Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309

    [24]

    Gandon S, Day T 2008 Vaccine 26 54

    [25]

    Ball F G, Knock E S, O’Neill P D 2008 Math. Biosci. 216 100

    [26]

    Wang Y B, Xiao G X, Hu J, Cheng T H, Wang L S 2009 Physica A 388 2535

    [27]

    Xiao S, Xiao G, Cheng T H 2008 IEEE Commun. Mag. 46 146

    [28]

    Gandon S, Mackinnon M, Nee S, Read A 2003 Proc. Roy. Soc. Lond. B 270 1129

    [29]

    Ganusov V V, Antia R 2006 Evolution 60 957

    [30]

    Newman M E J 2002 Phys. Rev. Lett. 89 208701

    [31]

    Barabsi A L, Albert R, Jeong H 1999 Physica A 272 173

    [32]

    Takeuchi Y, Ma W B, Beretta E 2000 Nonl. Anal. 42 931

    [33]

    Barabsi A L, Albert R 2002 Rev. Mod. Phys. 74 47

    [34]

    Abramowitz M, Stegun I 1972 Handbook of Mathematical Functions (New York: Dove Publisher)

  • [1]

    Li X, Wang X F 2006 IEEE Trans. Automatic Control 51 534

    [2]

    Li X, Wang X F 2007 Int. J. Syst. Sci. 38 400

    [3]

    Song Y R, Jiang G P 2009 Acta Phys. Sin. 58 5911 (in Chinese) [宋玉蓉、蒋国平 2009 物理学报 58 5911]

    [4]

    Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Xu W, Zhou T 2007 Phys. Lett. A 386 189

    [5]

    Pei W D, Chen Z Q, Yang Z Z 2008 Chin. Phys. B 17 373

    [6]

    Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A 2005 J. Theo. Bio. 235 275

    [7]

    Zhou T, Liu J G, Bai W J, Chen G R, Wang B H 2006 Phys. Rev. E 74 056109

    [8]

    Hayashi Y, Minoura M, Matsukubo J 2004 Phys. Rev. E 69 016112

    [9]

    Huang W, Jiang R, Hu M B, Wu Q S 2009 Chin. Phys. B 18 1306

    [10]

    Zhang H F, Michael S, Fu X C 2009 Commun. Theor. Phys. 52 180

    [11]

    Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200

    [12]

    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]

    [13]

    Watts D J, Strogatz S H 1998 Nature 393 440

    [14]

    Barabsi A L, Albert R 1999 Science 286 509

    [15]

    Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117

    [16]

    Lloyd A L, May R M 2001 Science 292 1316

    [17]

    Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 036104

    [18]

    Guo W P, Li X, Wang X F 2004 Physica A 380 684

    [19]

    Cohen R , Havlin S, ben-Avraham D 2003 Phys. Rev. Lett. 91 247901

    [20]

    Bose T, Trimper S 2009 Phys. Rev. E 79 051903

    [21]

    Gumel A B, McCluskey C C, van den Driessche P 2006 Bull. Math. Biol. 68 2105

    [22]

    Yip P, Watson R, Chen Q Z 2007 Statist. Med. 26 4475

    [23]

    Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309

    [24]

    Gandon S, Day T 2008 Vaccine 26 54

    [25]

    Ball F G, Knock E S, O’Neill P D 2008 Math. Biosci. 216 100

    [26]

    Wang Y B, Xiao G X, Hu J, Cheng T H, Wang L S 2009 Physica A 388 2535

    [27]

    Xiao S, Xiao G, Cheng T H 2008 IEEE Commun. Mag. 46 146

    [28]

    Gandon S, Mackinnon M, Nee S, Read A 2003 Proc. Roy. Soc. Lond. B 270 1129

    [29]

    Ganusov V V, Antia R 2006 Evolution 60 957

    [30]

    Newman M E J 2002 Phys. Rev. Lett. 89 208701

    [31]

    Barabsi A L, Albert R, Jeong H 1999 Physica A 272 173

    [32]

    Takeuchi Y, Ma W B, Beretta E 2000 Nonl. Anal. 42 931

    [33]

    Barabsi A L, Albert R 2002 Rev. Mod. Phys. 74 47

    [34]

    Abramowitz M, Stegun I 1972 Handbook of Mathematical Functions (New York: Dove Publisher)

  • [1] 何寿杰, 周佳, 渠宇霄, 张宝铭, 张雅, 李庆. 氩气空心阴极放电复杂动力学过程的模拟研究. 物理学报, 2019, 68(21): 215101. doi: 10.7498/aps.68.20190734
计量
  • 文章访问数:  7774
  • PDF下载量:  1794
  • 被引次数: 0
出版历程
  • 收稿日期:  2009-12-09
  • 修回日期:  2010-01-03
  • 刊出日期:  2010-05-05

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