基于元胞自动机考虑传播延迟的复杂网络病毒传播研究

王亚奇; 蒋国平

doi:10.7498/aps.60.080510

摘要

基于元胞自动机,研究传播延迟对复杂网络病毒传播动力学行为的影响,提出一种新的易染状态-感染状态-易染状态(SIS)传播模型.研究表明,传播延迟的存在显著降低了网络的传播临界值,增强了网络中病毒爆发的危险性.研究还发现,随着传播延迟的增大,病毒的感染程度以及传播速率都明显增大.此外,SIS传播模型不仅能够反映病毒的平均传播趋势,而且可以描述病毒随时间的动态演化过程以及病毒的爆发和消亡等概率事件,从而有效地克服了利用平均场方法构建的微分方程模型只能反映病毒平均传播趋势的局限性.同时,还给出有效控制网络中病毒传

关键词:

Abstract

In this paper, based on the cellular automata, we propose a new susceptible-infected-susceptible (SIS) model to study epidemic spreading in the networks with spreading delay. Theoretical analysis and simulation results show that the existence of spreading delay can significantly reduce the epidemic threshold and enhance the risk of outbreak of epidemics. It is also found that both the epidemic prevalence and the propagation velocity increase obviously with the spreading delay increasing. Moreover, the SIS model proposed in this paper describes not only the average propagation tendency of epidemics, but also the dynamic evolution process over the time of epidemics and the probability events such as outbreak and extinction of epidemics, and thus can overcome the limitations of the differential equation model based on mean-field method that describes only the average transmitting tendency of epidemics. Meanwhile, some suggestions of how to effectively control the propagation of epidemics are presented.

Keywords:

作者及机构信息

1.
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 (CX10B-193Z) 资助的课题.

Authors and contacts

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

参考文献

[1]	Newman M E J 2003 SIAM Rev. 45 167
[2]
[3]	Dorogovtsev S N, Goltsev A V, Mendes J F F 2008 Rev. Mod. Phys. 80 1275
[4]	Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
[5]
[6]	Kermack W O, McKendrick A G 1927 Proc. Roy. Soc. 115 700
[7]
[8]
[9]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[10]	Watts D J, Strogatz S H 1998 Nature 393 440
[11]
[12]	Bailey N T J 1993 The Mathematical Theory of Infectious Diseases (Berlin: Springer-Verlag)
[13]
[14]
[15]	Barabsi A L, Albert R 1999 Science 286 509
[16]
[17]	Albert R, Barabsi A L 2000 Phys. Rev. Lett. 85 24
[18]	Xu X J, Chen G R 2009 Int. J. Bifur. Chaos 19 623
[19]
[20]
[21]	Xia C Y, Liu Z X, Chen Z Q, Sun S W, Yuan Z Z 2008 Front. Electr. Electron. Eng. China 3 129
[22]	Wang Y Q, Jiang G P 2010 Acta Phys. Sin. 59 6724 (in Chinese) [王亚奇、蒋国平 2010 59 6724]
[23]
[24]	Tchuenche J M, Nwagwo A, Levins R 2007 Math. Meth. Appl. Sci. 30 733
[25]
[26]
[27]	Zaman G, Kang Y H, Jung H 2009 Biosystems 98 43
[28]
[29]	Briat C, Varriest E L 2009 Biomed. Signal Proces. 4 272
[30]
[31]	Fuentes M A, Kuperman M N 1999 Physica A 267 471
[32]	Sirakoulis G C, Karafyllidis I, Thanailakis A 2000 Ecol. Model. 133 209
[33]
[34]
[35]	White S H, del Rey A M, Snchez G R 2009 Appl. Math. Sci. 3 959
[36]
[37]	Jin Z, Liu Q X, Mainul H 2007 Chin. Phys. 16 1267
[38]	Song Y R, Jiang G P 2009 Acta Phys. Sin. 58 5911 (in Chinese) [宋玉蓉、蒋国平 2009 58 5911]
[39]
[40]	Gagliardi H, Alves D 2010 Math. Popul. Stud. 17 79
[41]
[42]
[43]	Willox R, Grammaticos B, Carstea A S, Ramani A 2003 Physica A 328 13
[44]
[45]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[46]
[47]	Newman M E J 2002 Phys. Rev. Lett. 89 208701
[48]	El Yacoubi S, Jai A 2002 Math. Comput. Modell. 36 1059
[49]
[50]
[51]	Solomonoff R, Rapoport A 1951 Bull. Math. Biophys. 13 107
[52]	Liu Q X, Jin Z 2005 Chin. Phys. 14 1370
[53]
[54]	Wang Y B, Xiao G X, Hu J, Cheng T H, Wang L S 2009 Physica A 388 2535
[55]
[56]
[57]	Xu X J, Peng H O, Wang X M, Wang Y H 2006 Physica A 367 525
[58]	Ierace N, Urrutia C, Bassett R 2005 Ubiquity 6 2
[59]
[60]
[61]	Park J, Sahni S 2005 Trans. Comput. 54 1081

施引文献

[1]	Newman M E J 2003 SIAM Rev. 45 167
[2]
[3]	Dorogovtsev S N, Goltsev A V, Mendes J F F 2008 Rev. Mod. Phys. 80 1275
[4]	Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 3309
[5]
[6]	Kermack W O, McKendrick A G 1927 Proc. Roy. Soc. 115 700
[7]
[8]
[9]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[10]	Watts D J, Strogatz S H 1998 Nature 393 440
[11]
[12]	Bailey N T J 1993 The Mathematical Theory of Infectious Diseases (Berlin: Springer-Verlag)
[13]
[14]
[15]	Barabsi A L, Albert R 1999 Science 286 509
[16]
[17]	Albert R, Barabsi A L 2000 Phys. Rev. Lett. 85 24
[18]	Xu X J, Chen G R 2009 Int. J. Bifur. Chaos 19 623
[19]
[20]
[21]	Xia C Y, Liu Z X, Chen Z Q, Sun S W, Yuan Z Z 2008 Front. Electr. Electron. Eng. China 3 129
[22]	Wang Y Q, Jiang G P 2010 Acta Phys. Sin. 59 6724 (in Chinese) [王亚奇、蒋国平 2010 59 6724]
[23]
[24]	Tchuenche J M, Nwagwo A, Levins R 2007 Math. Meth. Appl. Sci. 30 733
[25]
[26]
[27]	Zaman G, Kang Y H, Jung H 2009 Biosystems 98 43
[28]
[29]	Briat C, Varriest E L 2009 Biomed. Signal Proces. 4 272
[30]
[31]	Fuentes M A, Kuperman M N 1999 Physica A 267 471
[32]	Sirakoulis G C, Karafyllidis I, Thanailakis A 2000 Ecol. Model. 133 209
[33]
[34]
[35]	White S H, del Rey A M, Snchez G R 2009 Appl. Math. Sci. 3 959
[36]
[37]	Jin Z, Liu Q X, Mainul H 2007 Chin. Phys. 16 1267
[38]	Song Y R, Jiang G P 2009 Acta Phys. Sin. 58 5911 (in Chinese) [宋玉蓉、蒋国平 2009 58 5911]
[39]
[40]	Gagliardi H, Alves D 2010 Math. Popul. Stud. 17 79
[41]
[42]
[43]	Willox R, Grammaticos B, Carstea A S, Ramani A 2003 Physica A 328 13
[44]
[45]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[46]
[47]	Newman M E J 2002 Phys. Rev. Lett. 89 208701
[48]	El Yacoubi S, Jai A 2002 Math. Comput. Modell. 36 1059
[49]
[50]
[51]	Solomonoff R, Rapoport A 1951 Bull. Math. Biophys. 13 107
[52]	Liu Q X, Jin Z 2005 Chin. Phys. 14 1370
[53]
[54]	Wang Y B, Xiao G X, Hu J, Cheng T H, Wang L S 2009 Physica A 388 2535
[55]
[56]
[57]	Xu X J, Peng H O, Wang X M, Wang Y H 2006 Physica A 367 525
[58]	Ierace N, Urrutia C, Bassett R 2005 Ubiquity 6 2
[59]
[60]
[61]	Park J, Sahni S 2005 Trans. Comput. 54 1081

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