多关系网络上的流行病传播动力学研究

李睿琪; 唐明; 许伯铭

doi:10.7498/aps.62.168903

摘要

多关系网络已经吸引了许多人的注意, 目前的研究主要涉及其拓扑结构及其演化的分析、不同类型关系的挖掘、重叠社区的检测、级联失效动力学等. 然而,多关系网络上流行病传播的研究还相对较少. 由此提出一种双关系网络模型(工作-朋友关系网), 研究多关系对于流行病传播动力学行为的影响. 在全接触模式下, 多关系的存在会显著降低网络中的爆发阈值, 使得疾病更容易流行而难以控制. 对比ER (Erdös-Rènyi), WS (Watts-Strogatz), BA (Barabási-Albert)三种网络, 由于结构异质性的差异, WS网络受到的影响最大, ER网络次之, BA网络最小. 有趣的是, 其爆发阈值的相对变化大小与网络结构无关. 在单点接触模式下, 增加强关系的权重将显著提升爆发阈值, 降低感染密度; 随着强关系的比例变化将出现最优值现象: 极大的爆发阈值和极小的感染密度. 随着强关系的边权增加, 达到最优值的边比例将减少. 更为有趣的是, 三个网络中优值出现的位置几乎一致, 独立于网络结构. 这一研究不但有助于理解多关系网络上的病毒传播过程, 也为多关系网络研究提供了一个新的视角.

关键词:

Abstract

Networks with links representing different relationships have attracted much attention in recent years. Previous studies mostly focused on the analyses of network topology and evolution, multi-relation pattern mining, detection of overlapping communities, and cascading failure. However, epidemic spreading on multi-relation networks remains a largely unexplored area. We propose a binary-relation network model, representing working and friendship relationships, to reveal the effect of multiple relationships on the epidemic spreading. A link representing a closer relationship carries a higher weight. For reactive infection process in a multi-relation network, the threshold of outbreak is suppressed, making the epidemic harder to control. Comparing the networks with different structural heterogeneities such as the Watts-Strogatz (WS), Erdös-Rènyi and Barabási-Albert networks, the WS network is affected most significantly. Interestingly, the relative changes in the thresholds on the three networks are found to be independent of the structure. For contact infection process, an increase in the weight of the closer relationship can raise the outbreak threshold significantly and reduce the prevalence. As the fraction of closer relationship varies, an optimal fraction corresponding to a maximum outbreak threshold and minimum prevalence emerges. With an increase in the weight of the closer relationship, the proportion of links corresponding to the optimal value decreases. Most interestingly, the optimal proportions of closer-relation links on the three networks are almost the same, and thus they are independent of the network topology. This study not only contributes to the better understanding of epidemic spreading dynamics on multi-relation networks, but also provides a new perspective for research on multi-relation networks.

Keywords:

作者及机构信息

1.
电子科技大学互联网科学中心, 成都 610054;

2.
香港中文大学物理系, 香港

基金项目: 国家自然科学基金(批准号: 11105025);博士后科学基金特别资助(批准号: 2012T50711);博士后科学基金(批准号: 20110491705);博士点新教师基金 (批准号: 20110185120021);香港特别行政区研究资助局项目(批准号: CUHK-401109);电子科技大学计算机学院银杏黄创新基金和电子科技大学第七期大学生创新基金资助的课题.

Authors and contacts

1.
Web Science Center, University of Electronic Science and Technology of China, Chengdu 610054, China;

2.
Department of Physics, The Chinese University of Hong Kong, Hong Kong, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11105025), the China Postdoctoral Science Special Foundation (Grant No. 2012T50711), the China Postdoctoral Science Foundation (Grant No. 20110491705), the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 20110185120021), the Project of Research Grants Council of the Hong Kong Special Administrative Region Government, China (Grant No. CUHK-401109), the Yinxinghuang Innovation Fund Aroused by School of Computer Science and Technology, University of Electronic Science and Technology of China, and the 7th Academician Innovation Fund of University of Electronic Science and Technology of China.

参考文献

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[10]	Colizza V, Barrat A, Barthelemy M, Vespignani A 2006 Proc. Natl. Acad. Sci. 103 2015
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[17]	Palla G, Derenyi I, Farkas I, Vicsek T 2005 Nature 435 814
[18]	Szell M, Lambiotte R, Thurner S 2010 Proc. Natl. Acad. Sci. 107 13636
[19]	Parshani R, Buldyrev S V, Havlin S 2011 Proc. Natl. Acad. Sci. 108 1007
[20]	Buldyrev S V, Parshani R, Paul G, Stanley H E, Havlin S 2010 Nature 464 1025
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[26]	Liu J P, Microbiol J 2006 Iummunol. Infect. 39 4
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[33]	Barabási A L, Albert R 1999 Science 286 509
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[41]	Castellano C, Pastor-Satorras R 2012 Sci. Rep. 2 371
[42]	Pajevic S, Plenz D 2012 Nature Phys. 8 429
[43]	Shu P P, Tang M, Gong K, Liu Y 2012 Chaos 22 043124
[44]	Gong K, Tang M, Yang H, Shang M S 2011 Chaos 21 043130
[45]	Castellano C, Pastor-Satorras R 2006 Phys. Rev. Lett. 96 038701
[46]	Perez-Reche F J, Ludlam J J, Taraskin S N, Gilligan C A 2011 Phys. Rev. Lett. 106 218701
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[48]	Gong K, Tang M, Shang M S, Zhou T 2012 Acta Phys. Sin. 61 098901 (in Chinese) [龚凯, 唐明, 尚明生, 周涛2012 61 098901]
[49]	Tian L, Di Z R, Yao H 2011 Acta Phys. Sin. 60 28901 (in Chinese) [田柳, 狄增如, 姚虹 2011 60 28901]
[50]	Fan Y, Di Z R, Chen H B, Fang J Q 2009 Acta Phys. Sin. 58 1383 (in Chinese) [樊瑛, 狄增如, 陈宏斌, 方锦清 2009 58 1383]

施引文献

[1]	Anderson R M, May R M 1992 Infectious Disease of Humans (Oxford: Oxford University Press)
[2]	Dailey D J, Gani J 2001 Epidemic Modeling: An Introduction (Cambridge: Cambridge University Press)
[3]	Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175
[4]	Newman M E J 2010 Networks: An Introduction (Oxford: Oxford University Press)
[5]	Dorogovtsev S N, Goltsev A V, Mendes J F F 2008 Rev. Mod. Phys. 80 1275
[6]	Barrat A, Barthelmy M, Vespignani A 2008 Dynamical Processes on Complex Networks (New York: Cambridge University Press)
[7]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[8]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[9]	Hufnagel L, Brockmann D, Geisel T 2004 Proc. Natl. Acad. Sci. 101 15124
[10]	Colizza V, Barrat A, Barthelemy M, Vespignani A 2006 Proc. Natl. Acad. Sci. 103 2015
[11]	Balcan D, Hu H, Goncalves B, Bajardi P, Poletto C, Ramasco J J, Paolotti D, Perra N, Tizzoni M, Broeck W V, Colizza V, Vespignani A 2009 BMC Medicine 7 45
[12]	Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47
[13]	Barabási A L 2009 Science 325 412
[14]	Cai D, Shao Z, He X F, Yan X F, Han J W 2005 PKDD Porto, Portugal, October 3-7, 2005 p446
[15]	Stroele V, Oliveira J, Zimbrão G, Souza J M 2009 International Conference on Computational Science and Engineering Vancouver, Canada, August 29-31 2009 p711
[16]	Cai D Shao Z, He X F, Yan X F, Han J W 2005 LinkKDD Chicago, USA August 21, 2005 p58
[17]	Palla G, Derenyi I, Farkas I, Vicsek T 2005 Nature 435 814
[18]	Szell M, Lambiotte R, Thurner S 2010 Proc. Natl. Acad. Sci. 107 13636
[19]	Parshani R, Buldyrev S V, Havlin S 2011 Proc. Natl. Acad. Sci. 108 1007
[20]	Buldyrev S V, Parshani R, Paul G, Stanley H E, Havlin S 2010 Nature 464 1025
[21]	Magnani M, Rossi L 2011 International Conference on Advances in Social Networks Analysis and Mining Kaohsiung, Taiwan, China July 25-27, 2011 p7
[22]	Brummitt C D, Lee K M, Goh K I 2012 Phys. Rev. E 85 045102(R)
[23]	Albert R, Jeong H, Barabási A L 2000 Nature 406 378
[24]	Purcell D W, Parsons J T, Halkitis P N, Mizuno Y, Woods W J 2001 J. Subst Abuse 13 185
[25]	Wolitski R J, Fenton K A 2011 AIDS Behav. 15 9
[26]	Liu J P, Microbiol J 2006 Iummunol. Infect. 39 4
[27]	Onnela J P, Saramaki J, Hyvonen J, Szabo G, Lazer D, Kaski K, Kertesz J, Barabasi A L 2007 Proc. Natl. Acad. Sci. 104 7332
[28]	Wuchty S, Uzzi B 2011 PLoS ONE 6 e26972
[29]	Tasgin M, Bingol H O 2012 Advs. Complex Syst. 15 1250061
[30]	Yagan O, Gligor V 2012 Phys. Rev. E 86 036103
[31]	Erdös P, Rényi A 1959 Publications Mathematicae 6 290
[32]	Watts D J, Strogatz S H 1998 Nature 393 440
[33]	Barabási A L, Albert R 1999 Science 286 509
[34]	Schumm P, Scoglio C, Gruenbacher D, Easton T 2007 Bio-Inspired Models of Network, Information and Computing Systems Bionetics Budapest, Hungary, December 10-12 2007 p202
[35]	Parshani R, Carmi S, Havlin S 2010 Phys. Rev. Lett. 104 258701
[36]	Cohen R, Erez K, Avraham D B, Havlin S 2000 Phys. Rev. Lett. 85 4626
[37]	Madar N, Kalisky T, Cohen R, Ben-Avraham D, Havlin S 2004 Eur. Phys. J. B 38 269
[38]	Gomez S, Arenas A, Borge-Holthoefer J, Meloni S, Moreno Y 2010 Europhys. Lett. 89 38009
[39]	Gomez S, Gomez-Gardenes J, Moreno Y, Arenas A 2011 Phys. Rev. E 84 036105
[40]	Castellano C, Pastor-Satorras R 2010 Phys. Rev. Lett. 105 218701
[41]	Castellano C, Pastor-Satorras R 2012 Sci. Rep. 2 371
[42]	Pajevic S, Plenz D 2012 Nature Phys. 8 429
[43]	Shu P P, Tang M, Gong K, Liu Y 2012 Chaos 22 043124
[44]	Gong K, Tang M, Yang H, Shang M S 2011 Chaos 21 043130
[45]	Castellano C, Pastor-Satorras R 2006 Phys. Rev. Lett. 96 038701
[46]	Perez-Reche F J, Ludlam J J, Taraskin S N, Gilligan C A 2011 Phys. Rev. Lett. 106 218701
[47]	Ma L J, Tang M, Liang X M 2009 Acta Phys. Sin. 58 83 (in Chinese) [马丽娟, 唐明, 梁小明 2009 58 83]
[48]	Gong K, Tang M, Shang M S, Zhou T 2012 Acta Phys. Sin. 61 098901 (in Chinese) [龚凯, 唐明, 尚明生, 周涛2012 61 098901]
[49]	Tian L, Di Z R, Yao H 2011 Acta Phys. Sin. 60 28901 (in Chinese) [田柳, 狄增如, 姚虹 2011 60 28901]
[50]	Fan Y, Di Z R, Chen H B, Fang J Q 2009 Acta Phys. Sin. 58 1383 (in Chinese) [樊瑛, 狄增如, 陈宏斌, 方锦清 2009 58 1383]

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