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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 >.
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Keywords:
- complex networks /
- epidemic spreading /
- susceptible-infected-susceptible model /
- actual betweenness
[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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[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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