疾病传播与级联失效相互作用的研究:度不相关网络中疾病扩散条件的分析

欧阳博; 金心宇; 夏永祥; 蒋路茸; 吴端坡

doi:10.7498/aps.63.218902

摘要

在网络科学中,对疾病传播和级联失效的研究分属两个独立的领域,但在实际中存在许多两个过程相互耦合的情况. 比如在通信网络中,病毒传播会对数据传输造成影响,导致网络中负载变化,进而可能引发级联失效. 这个现象已被观察到. 通过建立两个动态过程相互作用的模型及针对该模型的分析,本文给出了计入节点的负载和容量时疾病爆发的条件. 这一条件是由描述疾病传播速率的传播概率与描述节点容量大小的冗余系数共同决定的. 进一步探讨表明,当疾病传播速率一定而冗余系数变化时,疾病恰好开始传播的临界点附近未感染且未失效的节点的数量是最大的,即在此点上网络处于最佳工作状态. 因此给出疾病爆发的临界条件具有重要意义.

关键词:

Abstract

Epidemics and cascades are independently studied topics in network science, but in practice, there are cases where they interact and neither of their effects can be ignored, e.g., when a digital virus spreads in a communication network that is transferring data. We have built a model to study their interplay in previous works. Here we present the epidemic threshold criteria of this model. When the infectivity is fixed, the tolerance parameter , in capturing the capacity of nodes, must be larger than a critical value to fulfill the criteria, and at equilibrium the fraction of nodes both uninfected and un-failed is the largest at this critical point. So the the presentation of the epidemic threshold criteria is of significance.

Keywords:

作者及机构信息

1.
浙江大学电子电路与信息系统研究所, 杭州 310027

基金项目: 国家自然科学基金(批准号:61174153)资助的课题.

Authors and contacts

1.
Department of Information Science and Electronic Engineering, Zhejiang University, Hongzhou 310027, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61174153).

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施引文献

[1]	Kermark M, Mckendrick A 1932 Proc. R. Soc. Lond. A 138 55
[2]
[3]	Bailey N T 1975 The Mathematical Theory of Infectious Diseases and its Applications (High Wycombe, Bucks: Charles Griffin Company Ltd)
[4]
[5]	Liu Z, Hu B 2005 Europhys. Lett. 72 315
[6]
[7]	Del Genio C I, House T 2013 Phys. Rev. E 88 040801
[8]	Guo D, Trajanovski S, Van de Bovenkamp R, Wang H, Van Mieghem P 2013 Phys. Rev. E 88 042802
[9]
[10]
[11]	Hernndez D G, Risau-Gusman S 2013 Phys. Rev. E 88 052801
[12]	Huang B, Zhao X Y, Qi K, Tang M, Do Y 2013 Acta Phys. Sin. 62 218902 (in Chinese) [黄斌, 赵翔宇, 齐凯, 唐明, 都永海 2013 物理学报 62 218902]
[13]
[14]
[15]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[16]
[17]	Zhou J, Liu Z, Li B 2007 Phys. Lett. A 368 458
[18]
[19]	Pastor-Satorras R, Vespignani A 2005 Handbook of graphs and networks: from the genome to the internet (Wiley) p111
[20]
[21]	Sachtjen M, Carreras B, Lynch V 2000 Phys. Rev. E 61 4877
[22]
[23]	Kinney R, Crucitti P, Albert R, Latora V 2005 Eur. Phys. J. B 46 101
[24]
[25]	Cohen R, Erez K, Ben-Avraham D, Havlin S 2000 Phys. Rev. Lett. 85 4626
[26]
[27]	Huang X, Vodenska I, Havlin S, Stanley H E 2013 Sci. Rep. 3 1219
[28]	Borrvall C, Ebenman B, Jonsson T 2000 Ecol. Lett. 3 131
[29]
[30]
[31]	Motter A E, Lai Y C 2002 Phys. Rev. E 66 065102
[32]
[33]	Xia Y, Fan J, Hill D 2010 Physica A 389 1281
[34]	Goh K I, Lee D S, Kahng B, Kim D 2003 Phys. Rev. Lett. 91 148701
[35]
[36]
[37]	Hoore M, Moghimi-Araghi S 2013 J. Phys. A: Math. Gen. 46 195001
[38]	Moreno Y, Gmez J, Pacheco A 2002 Europhys. Lett. 58 630
[39]
[40]
[41]	Kim D H, Kim B J, Jeong H 2005 Phys. Rev. Lett. 94 025501
[42]	Lee D S, Goh, K I, Kahng B, Kim D 2004 Physica A 338 84
[43]
[44]	Erds P, Rnyi A 1960 Publ. Math. Inst. Hongar. Acad. Sci. 5 17
[45]
[46]	Barabsi A L, Albert R 1999 Science 286 509
[47]
[48]	Gross T, D' Lima C J D, Blasius B 2006 Phys. Rev. Lett. 96 208701
[49]
[50]
[51]	Shaw L B, Schwartz I B 2008 Phys. Rev. E 77 066101
[52]	Dickison M, Havlin S, Stanley H E 2012 Phys. Rev. E 85 066109
[53]
[54]	Saumell-Mendiola A, Serrano M , Bogu M 2012 Phys. Rev. E 86 026106
[55]
[56]	Funk S, Jansen V A A 2010 Phys. Rev. E 81 036118
[57]
[58]
[59]	Ni S, Weng W, Zhang H 2011 Physica A 390 4528
[60]
[61]	Shang Y 2013 Int. J. Biomath. 6 1350007
[62]	Hu K, Hu T, Tang Y 2010 Chin. Phys. B 19 080206
[63]
[64]
[65]	Schimit P, Monteiro L 2011 Ecol. Model. 222 1651
[66]	Zhang H F, Yang Z, Wu Z X, Wang B H, Zhou T 2013 Sci. Rep. 3 3292
[67]
[68]	Wang Z, Zhang H, Wang Z 2014 Chaos Soliton. Fract. 6 1
[69]
[70]
[71]	Meloni S, Gmez-Gardees J 2010 Phys. Rev. E 82 056105
[72]
[73]	Morris R G, Barthelemy M 2012 Phys. Rev. Lett. 109 128703
[74]
[75]	Coffman E Jr, Ge Z, Misra V, Towsley D 2002 Proceedings of the 40th Annual Allerton Conference on Communications, Computing and Control, Urbana, USA, October 2-4, 2002 p1
[76]	Ouyang B, Jin X, Xia Y, Jiang L, Wu D 2014 Europhys. Lett. 106 28005
[77]
[78]
[79]	Jiang L, Jin X, Xia Y, Ouyang B, Wu D 2014 arXiv:1405.3009 [physics.soc-ph]
[80]
[81]	Dobson I, Carreras B A, Newman D E 2005 Probab. Eng. Inform. Sc. 19 15
[82]	Sansavini G, Hajj M, Puri I, Zio E 2009 Europhys. Lett. 87 48004
[83]
[84]	Ouyang B, Jin X, Xia Y, Jiang L 2014 Eur. Phys. J. B 87 1
[85]
[86]	Newman M E J 2002 Phys. Rev. E 66 016128
[87]
[88]
[89]	Moreno Y, Pastor-Satorras R, Vespignani A 2002 Eur. Phys. J. B 26 521

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