Dynamic interplay between epidemics and cascades:Epidemic outbreaks in uncorrelated networks

Ouyang Bo; Jin Xin-Yu; Xia Yong-Xiang; Jiang Lu-Rong; Wu Duan-Po

doi:10.7498/aps.63.218902

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:

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).

References

[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

Cited By

[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

[1]	Yan Yu-Wei, Jiang Yuan, Yang Song-Qing, Yu Rong-Bin, Hong Cheng. Network failure model based on time series. Acta Physica Sinica, 2022, 71(8): 088901. doi: 10.7498/aps.71.20212106
[2]	. Cascading failures on complex networks with weak interdependency groups. Acta Physica Sinica, 2022, (): . doi: 10.7498/aps.71.20210850
[3]	Pan Qian-Qian, Liu Run-Ran, Jia Chun-Xiao. Cascading failures on complex networks with weak interdependency groups. Acta Physica Sinica, 2022, 71(11): 110505. doi: 10.7498/aps.70.20210850
[4]	Jiang Wen-Jun, Liu Run-Ran, Fan Tian-Long, Liu Shuang-Shuang, Lü Lin-Yuan. Overview of precaution and recovery strategies for cascading failures in multilayer networks. Acta Physica Sinica, 2020, 69(8): 088904. doi: 10.7498/aps.69.20192000
[5]	Han Wei-Tao, Yi Peng, Ma Hai-Long, Zhang Peng, Tian Le. Robustness of interdependent networks withheterogeneous weak inter-layer links. Acta Physica Sinica, 2019, 68(18): 186401. doi: 10.7498/aps.68.20190761
[6]	Han Wei-tao, Yi Peng. Percolation of interdependent networks with conditional dependency clusters. Acta Physica Sinica, 2019, 68(7): 078902. doi: 10.7498/aps.68.20182258
[7]	Ruan Yi-Run, Lao Song-Yang, Wang Jun-De, Bai Liang, Hou Lü-Lin. An improved evaluating method of node spreading influence in complex network based on information spreading probability. Acta Physica Sinica, 2017, 66(20): 208901. doi: 10.7498/aps.66.208901
[8]	Su Zhen, Gao Chao, Li Xiang-Hua. Analysis of the effect of node centrality on diffusion mode in complex networks. Acta Physica Sinica, 2017, 66(12): 120201. doi: 10.7498/aps.66.120201
[9]	Shu Pan-Pan, Wang Wei, Tang Ming, Shang Ming-Sheng. Discriminability of node influence in flower fractal scale-free networks. Acta Physica Sinica, 2015, 64(20): 208901. doi: 10.7498/aps.64.208901
[10]	Li Zhao, Guo Yan-Hui, Xu Guo-Ai, Hu Zheng-Ming. Analysis of cascading dynamics in complex networks with an emergency recovery mechanism. Acta Physica Sinica, 2014, 63(15): 158901. doi: 10.7498/aps.63.158901
[11]	Duan Dong-Li, Zhan Ren-Jun. Evolution mechanism of node importance based on the information about cascading failures in complex networks. Acta Physica Sinica, 2014, 63(6): 068902. doi: 10.7498/aps.63.068902
[12]	Chen Shi-Ming, Zou Xiao-Qun, Lü Hui, Xu Qing-Gang. Research on robustness of interdependent network for suppressing cascading failure. Acta Physica Sinica, 2014, 63(2): 028902. doi: 10.7498/aps.63.028902
[13]	Yuan Ming. A cascading failure model of complex network with hierarchy structure. Acta Physica Sinica, 2014, 63(22): 220501. doi: 10.7498/aps.63.220501
[14]	Ren Zhuo-Ming, Liu Jian-Guo, Shao Feng, Hu Zhao-Long, Guo Qiang. Analysis of the spreading influence of the nodes with minimum K-shell value in complex networks. Acta Physica Sinica, 2013, 62(10): 108902. doi: 10.7498/aps.62.108902
[15]	Huang Bin, Zhao Xiang-Yu, Qi Kai, Tang Ming, Do Younghae. Coloring the complex networks and its application for immunization strategy. Acta Physica Sinica, 2013, 62(21): 218902. doi: 10.7498/aps.62.218902
[16]	Fu Bai-Bai, Gao Zi-You, Lin Yong, Wu Jian-Jun, Li Shu-Bin. The analysis of traffic congestion and dynamic propagation properties based on complex network. Acta Physica Sinica, 2011, 60(5): 050701. doi: 10.7498/aps.60.050701
[17]	Wang Ya-Qi, Jiang Guo-Ping. Epidemic spreading in complex networks with spreading delay based on cellular automata. Acta Physica Sinica, 2011, 60(8): 080510. doi: 10.7498/aps.60.080510
[18]	Wang Ya-Qi, Jiang Guo-Ping. Virus spreading on complex networks with imperfect immunization. Acta Physica Sinica, 2010, 59(10): 6734-6743. doi: 10.7498/aps.59.6734
[19]	Song Yu-Rong, Jiang Guo-Ping. Research of malware propagation in complex networks based on 1-D cellular automata. Acta Physica Sinica, 2009, 58(9): 5911-5918. doi: 10.7498/aps.58.5911
[20]	Xu Dan, Li Xiang, Wang Xiao-Fan. An investigation on local area control of virus spreading in complex networks. Acta Physica Sinica, 2007, 56(3): 1313-1317. doi: 10.7498/aps.56.1313

Catalog

Vol. 63, Issue 21 - 2014-11-05

Metrics

Abstract views: 5771
PDF Downloads: 579
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板