考虑到很多现实网络具有社团结构和小世界特性,提出结构强度可调的具有社团结构的动态小世界网络模型,它能模拟现实生活中的本地接触和移动接触现象,并基于平均场理论,建立该网络上的SIR病毒传播模型。研究表明:社团间长程移动率越大,病毒传播临界值越小,传播规模越大;社团结构越强,传播临界值越大,即强社团结构抑制病毒传播;另外,加强对社团间长程移动的控制,对控制病毒爆发具有重要作用。
Since many real networks generally have community structures and characteristics of small world, we propose a dynamical small-world network model with strength-tunable community, which can describe the phenomena of local contacts and moving contacts in real life. Then we construct a SIR transmission model on the proposed network on the basis of mean-field theory. Simulations and analysis show that, with the increase of inter-community long range jump probabilities, the epidemic threshold will decrease. And the larger the community strength is, the larger the epidemic threshold will be. Namely, large community degree can reduce the spreading of the virus. Additionally, in order to suppress the epidemic spreading, it is effective to strengthen the control of inter-community long range jump.
[1] 李翔, 刘宗华, 汪秉宏. 网络传播动力学[J]. 复杂系统与复杂性科学, 2010, 7（2/3):33-37.
Li Xiang, Liu Zonghua, Wang Binghong. On spreading dynamics on networks[J]. Complex Systems and Complexity Science, 2010, 7（2/3):33-37.
[2] 王亚奇, 蒋国平. 复杂网络中考虑不完全免疫的病毒传播研究[J]. 物理学报, 2010, 59（10):6734-6743.
Wang Yaqi, Jiang Guoping. Virus spreading on complex networks with imperfect immunization[J]. Acta Physica Sinica, 2010, 59（10):6734-6743.
[3] Gong Y W, Song Y R, Jiang G P. Global dynamics of a novel multi-group model for computer worms[J]. Chinese Phy-sics B, 2013, 22（4):040204.
[4] Zhou J,Liu Z H,Li B W.Influence of network structure on rumor propagation[J].Physics Letters A,2007,368（6):458-463.
[5] Huang W, Li C G. Epidemic spreading in scale-free networks with community structure[J]. Journal of Statistical Mechanics:Theory and Experiment, 2007, 2007（01):P01014.
[6] Liu Z H, Hu B. Epidemic spreading in community networks[J]. Europhysics Letters, 2005, 72（2):315-321.
[7] Wu X Y, Liu Z H. How community structure influences epidemic spreading in social networks[J]. Physica A, 2008, 387（2):623-630. SIR
[8] Zhang J P, Jin Z. Epidemic spreading on complex networks with community structure[J]. Applied Mathematics and Computation, 2012, 219（6):2829-2838.
[9] 樊瑛, 狄增如, 何大韧. 探讨社会网络理论与分析的几个问题[J].复杂系统与复杂性科学, 2010, 7（2/3):38-41.
Fan Ying, Di Zengru, He Da′ren. Some topics on social network theory and analysis[J]. Complex Systems and Complexity Science, 2010, 7（2/3):38-41.
[10] 韩筱璞, 汪秉宏, 周涛. 人类行为动力学研究[J]. 复杂系统与复杂性科学, 2010, 7（2-3):132-144.
Han Xiaopu, Wang Binghong, Zhou Tao. Researches of human dynamics[J]. Complex Systems and Complexity Science, 2010, 7（2/3):132-144.
[11] 张海峰, 王阳阳, 汪秉宏. 行为反应对复杂网络上传染病动力学的影响[J]. 复杂系统与复杂性科学, 2012, 9（3):13-21.
Zhang Haifeng, Wang Yangyang, Wang Binghong. The impacts of behavioral responses on the spread of infectious diseases on complex networks[J]. Complex Systems and Complexity Science, 2012, 9（3):13-21.
[12] Girvan M, Newman M E J. Community structure in social and biological networks[J]. PNAS, 2002, 99（12):7821-7826.
[13] Watts D J, Strogatz S H. Collective dynamics of ‘small-world’ networks[J]. Nature, 1998, 393（6684):440-442.
[14] Newman M E J, Watts D J. Renormalization group analysis of the small-world network model[J]. Physics Letters A, 1999, 263（4):341-346.
[15] Albert R, Barabási A L. Statistical mechanics of complex networks[J]. Reviews of modern physics, 2002, 74（1):47-97.
[16] Shao F, Jiang G P. Traffic driven epidemic spreading in homogeneous networks with community structure[J]. Journal of Networks, 2012, 7（5):850-855.
[17] Zhang H L, Guan Z H, Li T, et al. A stochastic SIR epidemic on scale-free network with community structure[J]. Physica A, 2013, 392（4):974-981.
[18] Chu X W, Guan J H, Zhang Z Z, et al. Epidemic spreading in weighted scale-free networks with community structure[J]. Journal of Statistical Mechanics:Theory and Experiment, 2009, 2009（07):P07043.
[19] Wang Y B, Xiao G X. Epidemics spreading in interconnected complex networks[J]. Physics Letters A, 2012, 376（42):2689-2696.
[20] Son S-W, Bizhani G, Christensen C, et al. Percolation theory on interdependent networks based on epidemic spreading[J]. Europhysics Letters, 2012, 97（1):16006.
[21] Yan G, Fu Z Q, Ren J, et al. Collective synchronization induced by epidemic dynamics on complex networks with communities[J]. Physical Review E, 2007, 75（1):016108.
[22] Sun H J, Gao Z Y. Dynamical behaviors of epidemics on scale-free networks with community structure[J]. Physica A, 2007, 381:491-496.
[23] Xia C Y, Sun S W, Rao F, et al. SIS model of epidemic spreading on dynamical networks with community[J]. Frontiers of Computer Science in China, 2009, 3（3):361-365.
[24] Zhou J, Liu Z H. Epidemic spreading in communities with mobile agents[J]. Physica A, 2009, 388:1228-1236.
[25] Saramäki J, Kaski K. Modelling development of epidemics with dynamic small-world networks[J]. Journal of Theoretical Biology, 2005, 234（3):413-421.
[26] Stone T E, Jones M M, McKay S R. Comparative effects of avoidance and vaccination in disease spread on dynamic small-world network[J]. Physica A, 2010, 389:5515-5520.
[27] Stone T E, McKay S R. Critical behavior of disease spread on dynamic small-world networks[J]. Europhysics Letters, 2011, 95（3):38003.
[28] Newman M E J, Girvan M. Finding and evaluating community structure in networks[J]. Physical Review E, 2004, 69（2):026113.
