无标度网络中最大传染能力限定的病毒传播问题研究  

Study of epidemic spreading on scale-free networks with finite maximum dissemination

作　　者：裴伟东[1,2] 刘忠信[1] 陈增强[1] 袁著祉[1] 

机构地区：[1]南开大学自动化系,天津300071 [2]天津师范大学计算机与信息工程学院,天津300387

出　　处：《物理学报》2008年第11期6777-6785,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:60774088);教育新世纪人才支持计划(批准号:NCET2005-229);教育部科学技术重点项目(批准号:107024);天津市市应用基础及前沿技术研究计划项目(批准号:08JCZDJC21900)资助的课题~~

摘　　要：传统的病毒传播模型在无限大无标度网络上不存在病毒传播阈值,即无论病毒的传播速率多么低,病毒始终能够在网络中传播.但研究发现,这个结论是在网络中存在超级传染者的假设下得到的,然而许多真实的无标度网络中并不存在超级传染者.因此,文章提出了一个最大传染能力限定的病毒传播模型,并从理论上证明了在最大传染能力限定的无限大无标度网络上,病毒传播阈值是存在的;同时,也分析了最大传染能力限定下非零传播阈值与有限规模网络下非零传播阈值的本质区别,并解释了为什么人们总是认为传统病毒传播模型对许多真实网络病毒感染程度估计过高的原因.Under the condition of infinite dissemination of the network,it has been proved that the classical epidemic models do not give epidemic thresholds in the infinite scale-free networks.That is,a disease can always propagate on the network no matter how low its spread speed.However,the ability of individuals to spread virus in many real networks is not always infinite.If the maximum dissemination of individuals in the network is set finite,then there should exist a non-zero epidemic threshold for the above epidemic models.The relations between the epidemic threshold and the maximum dissemination,the relations between the degree of infection and the maximum dissemination are discussed,meanwhile the reason why classical epidemic models always over-predict the degree of infections in real networks is explained.

关 键 词：无标度网络 最大传染能力 传播阈值 感染程度 

分 类 号：O157.5[理学—数学]