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不同于经典扩散模型中节点传染力等同于节点度k的假定, 基于交通流量的病毒扩散模型中, 各个节点的传染力可以等同于节点实际介数bk. 利用平均场近似方法, 提出基于交通流量SIS病毒修正扩散模型. 根据修正SIS模型, 以最小搜索信息路由为例, 重新研究病毒传播率β, 平均发包率λ同传播阈值βc, 平稳状态病毒密度ρ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, 传播阈值βc为实际介数bk的均值bk>与其平方的均值bk2>的比值. 而稳定状态时感染密度ρ同感染同病毒传播率β, 平均发包率λ 以及λ =1时节点实际介数的均值bλ=1> 的乘积倒数存在幂率关系.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
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[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 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 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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