基于交通流量的病毒扩散动力学研究  

Epidemic spreading on scale-free networks with traffic flow

作　　者：仇慎伟[1] 王开[2] 刘茜[2] 裴文江[2] 胡恒凯[1] 杨光[1] 蔚承建[1] 张毅锋[2] 

机构地区：[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

出　　处：《物理学报》2012年第15期1-7,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号: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);江苏省远程测控重点实验室开放基金(YCCK201005)资助的课题~~

摘　　要：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p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_k^2〉的比值.而稳定状态时感染密度p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.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 probabilityβ, traffic generation rate λ, epidemic thresholdβc, the stationary density of infected nodes p. Both theoretical analysis and experimental results show thatβc 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 p 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=l）.

关 键 词：复杂网络 病毒扩散 SIS模型 实际介数 

分 类 号：O157.5[理学—数学] O242.1[理学—基础数学]