基于交通流量的病毒扩散动力学研究

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b_k. 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β_c, 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β_c为实际介数b_k的均值<b_k>与其平方的均值<b_k²>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<b_λ=1> 的乘积倒数存在幂率关系.

Epidemic spreading on scale-free networks with traffic flow

The infectivity of a node is determined by its actual betweenness b_k 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 probabilityβ, traffic generation rate A,epidemic thresholdβ_c,the stationary density of infected nodes p.Both theoretical analysis and experimental results show thatβ_c is the ratio of the mean of the actual betweenness〈bk〉to its mean square〈b_k~2),when network topology and route strategy are given.Moreover,the stationary density of infected notes p behaves as power-law exponent with the reciprocal of the product of the spreading probabilityβ,the traffic generation rate A and the mean of the actual betweenness〈b_λ=1〉.