基于交通流量的病毒爆发动力行为研究

胡恒恺; 王开; 杨光; 刘茜; 裴文江; 仇慎伟; 蔚承建; 张毅锋

doi:10.7498/aps.61.200209

摘要

给出基于交通流量的病毒扩散易染-感染模型(SI)修正模型,进而利用平均场近似方法, 研究基于交通流量的病毒扩散动力学行为.以最小搜索信息路由为例, 重新研究了SI模型下扩散系数，τ与平均发包率λ、感染率β以及实际介数之间的关系. 理论分析与实验结果均表明,当网络拓扑和路由策略一定时,扩散参数τ反比于平均发包率λ和感染率β,是λ=1时的扩散参数τλ=1的1/λ.

关键词:

A modified susceptible-infected (SI) model is developed in this paper. The mean field approximation method is further adopted. This present research is based on traffic-driven epidemic spreading behavior. Take MIP routing for example, diffusion coefficient τ, traffic generation rate λ, infection rate β and their relationship with the actual betweenness bk are re-explored under the SI model. Both the theoretical and experimental results indicate that under the same internet topology and routing strategy, the diffusion coefficient τ is inversely proportional to average traffic generation rate λ and infection rate β.

Keywords:

作者及机构信息

1.
南京工业大学电子与信息工程学院, 南京 210009;

2.
东南大学信息科学与工程学院, 南京 210096

基金项目: 国家自然科学基金(批准号: 61201173, 60972165, 61105048, 60901012); 教育部博士点基金(批准号: 20100092120012, 20090092120012); 江苏省自然科学基金(批准号: BK2011060, BK2010240)和江苏省远程测控重点实验室开放基金(批准号: YCCK201005)资助的课题.

Authors and contacts

1.
College of Electronic and Information Engineering, Nanjing University of Technology, Nanjing 210009, China;

2.
Department of Radio Engineering, Southeast University, Nanjing 210096, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61201173, 60972165, 61105048, 60901012), the Doctoral Fund of Ministry of Education of China (Grant Nos. 20100092120012, 20090092120012), the Natural Science Foundation of Jiangsu Province, China (Grant Nos. BK2011060, BK2010240), and the Open Foundation of Key Laboratory of Remote Measuring and Control of Jiangsu Province, China (Grant No. YCCK201005).

参考文献

[1]	Watts D J, Strogatz S H 1998 Nature 393 440
[2]	Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 309
[3]	May R M, Lloyd A L 2001 Phys. Rev. E 64 066112
[4]	Barthelemy M, Barrat A, Pastor-Satorras R, Vespignani A 2004 Phys. Rev. Lett. 92 178701
[5]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[6]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[7]	Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 036104
[8]	Meloni S, Arenas A, Moreno Y 2009 Proc. Natl. Acad. Sci. USA. 106 16897
[9]	Wang Y Q, Jiang G P 2011 Acta Phys. Sin. 60 060202 (in Chinese) [王亚奇, 蒋国平 2011 物理学报 60 060202]
[10]	Qiu S W, Wang K, Liu Q, Pei W J, Hu H K, Yang G, Wei C J, Zhang Y F 2012 Acta Phys. Sin. 61 150201 (in Chinese) [仇慎伟, 王开, 刘茜, 裴文江, 胡恒凯, 杨光, 蔚承建, 张毅峰 2012 物理学报61 150201]
[11]	Barabasi A L, Albert R 2000 Physica A 281 69
[12]	Wang K, Zhang Y F, Zhou S Y, Pei W J, Li T, Wang S P 2011 Physica A 390 2593
[13]	Zhou SY, Wang K, Pei W J 2011 Chin. Phys. B 20 080501
[14]	Chen Y P, Paul G 2008 Phys. Rev. Lett. 101 058701
[15]	Maksim Ki, Lazaros K 2010 Nat. Phys. 6 888
[16]	Chen D B, Lu L Y 2012 Physica A 391 1777

施引文献

[1]	Watts D J, Strogatz S H 1998 Nature 393 440
[2]	Shi H J, Duan Z S, Chen G R, Li R 2009 Chin. Phys. B 18 309
[3]	May R M, Lloyd A L 2001 Phys. Rev. E 64 066112
[4]	Barthelemy M, Barrat A, Pastor-Satorras R, Vespignani A 2004 Phys. Rev. Lett. 92 178701
[5]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[6]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117
[7]	Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 036104
[8]	Meloni S, Arenas A, Moreno Y 2009 Proc. Natl. Acad. Sci. USA. 106 16897
[9]	Wang Y Q, Jiang G P 2011 Acta Phys. Sin. 60 060202 (in Chinese) [王亚奇, 蒋国平 2011 物理学报 60 060202]
[10]	Qiu S W, Wang K, Liu Q, Pei W J, Hu H K, Yang G, Wei C J, Zhang Y F 2012 Acta Phys. Sin. 61 150201 (in Chinese) [仇慎伟, 王开, 刘茜, 裴文江, 胡恒凯, 杨光, 蔚承建, 张毅峰 2012 物理学报61 150201]
[11]	Barabasi A L, Albert R 2000 Physica A 281 69
[12]	Wang K, Zhang Y F, Zhou S Y, Pei W J, Li T, Wang S P 2011 Physica A 390 2593
[13]	Zhou SY, Wang K, Pei W J 2011 Chin. Phys. B 20 080501
[14]	Chen Y P, Paul G 2008 Phys. Rev. Lett. 101 058701
[15]	Maksim Ki, Lazaros K 2010 Nat. Phys. 6 888
[16]	Chen D B, Lu L Y 2012 Physica A 391 1777

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