Epidemic spreading on scale-free networks with traffic flow

Qiu Shen-Wei; Wang Kai; Liu Qian; Pei Wen-Jiang; Hu Hen-Kai; Yang Guang; Wei Cheng-Jian; Zhang Yi-Feng

doi:10.7498/aps.61.150201

Abstract

The infectivity of a node is determined by its actual betweenness bk in the epidemic model based on traffic-flow other than degree k which is different from the classical epidemic models. Utilizing the mean-field theory, we propose a modified SIS epidemic model based on traffic-flow. With this model, taking MIP route as an example, we re-study the relationship among spreading probability β, traffic generation rate λ, epidemic threshold βc, the stationary density of infected nodes ρ. Both theoretical analysis and experimental results show that βc is the ratio of the mean of the actual betweenness bk > to its mean square bk2 >, when network topology and route strategy are given. Moreover, the stationary density of infected notes ρ behaves as power-law exponent with the reciprocal of the product of the spreading probability β , the traffic generation rate λ and the mean of the actual betweenness bλ=1 >.

Keywords:

complex networks /
epidemic spreading /
susceptible-infected-susceptible model /
actual betweenness

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. 60972165, 61105048, 60901012), the Doctoral Fund of Ministry of Education of China under (Grant Nos. 20100092120012, 20090092120012), the Natural Science Foundation of Jiangsu Province (Grant Nos. BK2011060, BK2010240), and the Open Fundation of Jiangsu Province Key Laboratory of Remote Measuring and Control (YCCK201005).

References

[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]	Barabasi A L, Albert R 2000 Physica A 281 69
[11]	Wang K, Zhang Y F, Zhou S Y, Pei W J, Li T, Wang S P 2011 Physica A 390 2593
[12]	Zhou SY, Wang K, Pei W J 2011 Chin. Phys. B 20 080501

Cited By

[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]	Barabasi A L, Albert R 2000 Physica A 281 69
[11]	Wang K, Zhang Y F, Zhou S Y, Pei W J, Li T, Wang S P 2011 Physica A 390 2593
[12]	Zhou SY, Wang K, Pei W J 2011 Chin. Phys. B 20 080501

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