移动环境下网络病毒传播模型及其稳定性研究

巩永旺; 宋玉蓉; 蒋国平

doi:10.7498/aps.61.110205

摘要

考虑网络节点的随机移动, 基于平均场理论提出一个移动环境下网络病毒传播的数学模型, 利用微分动力学系统理论研究了病毒传播行为. 研究表明, 当病毒基本再生数R0 1时, 网络中病毒逐渐消除, 系统的无病毒平衡点全局渐进稳定; 当R0 1时, 网络中病毒持续存在, 系统的地方病平衡点全局渐进稳定.通过仿真验证了所得结论的正确性.

关键词:

In this paper, considering the random motion of nodes, we propose an epidemic spreading model on network of mobile environment based on the mean-filed theory. Using the theory of differential dynamical system, the behaviors of epidemic spreading are further analyzed. It is shown that if R0 1, the epidemic always dies out and the disease-free equilibrium is globally asymptotically stable; and if R0 1, the epidemic is uniformly persistent and the endemic equilibrium is globally asymptotically stable. Numerical simulations are given to validate the results of theoretical analysis.

Keywords:

作者及机构信息

1.
南京邮电大学计算机学院, 南京 210003;

2.
南京邮电大学自动化学院, 南京 210003;

3.
盐城工学院信息工程学院, 盐城 224051

基金项目: 国家自然科学基金(批准号: 60874091)、江苏省六大人才高峰高层次人才项目(批准号: SJ209006)、高等学校博士点基金 (批准号: 20103223110003)、江苏省自然科学基金(批准号: BK2010526) 和江苏省研究生培养创新工程项目(批准号: CXLX11_0417, CXLX11_0403)资助的课题.

Authors and contacts

1.
College of Computer, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;

2.
College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;

3.
School of Information Engineering, Yancheng Institute of Technology, Yancheng 224051, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 60874091), the Six Projects Sponsoring Talent Summits of Jiangsu Province, China (Grant No. SJ209006), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103223110003), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010526), and the Graduate Student Innovation Research Project of Jiangsu Province, China (Grant Nos. CXLX11_0417, CXLX11_0403).

参考文献

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[2]	Song Y R, Jiang G P 2010 Acta Phys.Sin. 59 7546 (in Chinese) [宋玉蓉, 蒋国平 2010 物理学报 59 7546]
[3]	Wu Q C, Fu X C, Yang M 2011 Chin.Phys. B 20 046401
[4]	Pastor-Statorras R, Vespignani A 2001 Phys.Rev. E 63 066117
[5]	Castellano C, Pastor-Satorras R 2010 Phys.Rev.Lett.105 218701
[6]	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]
[7]	Shi H J, Duan Z S, Chen G R 2008 Physica A 387 2133
[8]	Wang Y Q, Jiang G P 2010 Acta Phys.Sin. 59 6734 (in Chinese) [王亚奇, 蒋国平 2010 物理学报 59 6734]
[9]	Ball F G, Knock E S, O'Neill P D 2008 Math.Biosci.216 100
[10]	Wang J Z, Liu Z R, Xu J H 2007 Physica A 382 715
[11]	Zhang H F, Fu X C 2009 Nonlinear Anal.: Theor. Meth. Appl. 70 3273
[12]	Pastor-Satorras R, Vespignani A 2001 Phys.Rev.E 65 036134
[13]	Madar N, Kalisky T, Cohen R, Been-Avraham, Havlin S 2004 Eur.Phys.J.B 38 269
[14]	Peng C B, Jin X G, Shi M X 2010 Physica A 389 549
[15]	Wang L, Zhu C P 2010 Phys. Proc. 3 1819
[16]	Wang P, Gonzalez M C, Hidalgo C A, Barabasi A L 2009 Science 324 1071
[17]	Buscarino A, Fortuna L, Frasca M, Latora V 2008 Euro. Phys. Lett. 82 38002
[18]	Frasca M, Buscarino A, Rizzo A, Fortuna L, Boccaletti S 2006 Phys.Rev.E 74 036110
[19]	Gonzalez M C, Herrmann H J 2004 Physica A 340 741
[20]	Rhodes C J, Nekovee M 2008 Physica A 387 6837
[21]	Yang H X, Wang W X, Xie Y B, Lai Y C, Wang B H 2011 Phys.Rev.E 83 016102
[22]	Van den Driessche P, Watmough J 2002 Math.Biosci. 180 29
[23]	Li M Y, Smith H L, Wang L 2001 SIAM J. Appl. Math. 62 58
[24]	Li M Y, Muldowney J S 1996 SIAM J.Math.Anal. 27 1070
[25]	Martin Jr R H 1974 J.Math.Anal.Appl. 45 432
[26]	Muldowney J S 1990 Rocky Mountain J. Math. 20 857
[27]	Xiang H J 2005 Appl.Math.J.Chin. Univ.Ser.A 20 284 (in Chinese) [向红军 2005 高校应用数学学报A辑 20 284]

施引文献

[1]	Zhou T, Liu J G, Bai W J, Chen G R, Wang B H 2006 Phys.Rev.E 74 056109
[2]	Song Y R, Jiang G P 2010 Acta Phys.Sin. 59 7546 (in Chinese) [宋玉蓉, 蒋国平 2010 物理学报 59 7546]
[3]	Wu Q C, Fu X C, Yang M 2011 Chin.Phys. B 20 046401
[4]	Pastor-Statorras R, Vespignani A 2001 Phys.Rev. E 63 066117
[5]	Castellano C, Pastor-Satorras R 2010 Phys.Rev.Lett.105 218701
[6]	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]
[7]	Shi H J, Duan Z S, Chen G R 2008 Physica A 387 2133
[8]	Wang Y Q, Jiang G P 2010 Acta Phys.Sin. 59 6734 (in Chinese) [王亚奇, 蒋国平 2010 物理学报 59 6734]
[9]	Ball F G, Knock E S, O'Neill P D 2008 Math.Biosci.216 100
[10]	Wang J Z, Liu Z R, Xu J H 2007 Physica A 382 715
[11]	Zhang H F, Fu X C 2009 Nonlinear Anal.: Theor. Meth. Appl. 70 3273
[12]	Pastor-Satorras R, Vespignani A 2001 Phys.Rev.E 65 036134
[13]	Madar N, Kalisky T, Cohen R, Been-Avraham, Havlin S 2004 Eur.Phys.J.B 38 269
[14]	Peng C B, Jin X G, Shi M X 2010 Physica A 389 549
[15]	Wang L, Zhu C P 2010 Phys. Proc. 3 1819
[16]	Wang P, Gonzalez M C, Hidalgo C A, Barabasi A L 2009 Science 324 1071
[17]	Buscarino A, Fortuna L, Frasca M, Latora V 2008 Euro. Phys. Lett. 82 38002
[18]	Frasca M, Buscarino A, Rizzo A, Fortuna L, Boccaletti S 2006 Phys.Rev.E 74 036110
[19]	Gonzalez M C, Herrmann H J 2004 Physica A 340 741
[20]	Rhodes C J, Nekovee M 2008 Physica A 387 6837
[21]	Yang H X, Wang W X, Xie Y B, Lai Y C, Wang B H 2011 Phys.Rev.E 83 016102
[22]	Van den Driessche P, Watmough J 2002 Math.Biosci. 180 29
[23]	Li M Y, Smith H L, Wang L 2001 SIAM J. Appl. Math. 62 58
[24]	Li M Y, Muldowney J S 1996 SIAM J.Math.Anal. 27 1070
[25]	Martin Jr R H 1974 J.Math.Anal.Appl. 45 432
[26]	Muldowney J S 1990 Rocky Mountain J. Math. 20 857
[27]	Xiang H J 2005 Appl.Math.J.Chin. Univ.Ser.A 20 284 (in Chinese) [向红军 2005 高校应用数学学报A辑 20 284]

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