网络病毒传播模型中的两个问题

Two Issues of Spreading Model for Network Viruses

现有的网络病毒分析模型大都依据流行病模型建立,这些模型并不能反映现代网络环境下病毒的传播规律,故有一些问题不能得到很好的解决。文章在新模型的基础上重点讨论其中的两个最为突出的问题:网络病毒的门限值问题和单节点在病毒传播中的不同作用。通过对新模型解的分析得出结论:如果病毒的传播紧密地依赖网络的连接率,而它们的治愈率又相对较小,那么这类病毒的门限值是不存在的。基于该结论文章对长期以来困扰网络病毒传播模型的两个公开的问题给出了合理的解释。文章将电脑的连接率作为节点的一个最基本的特征,从而指出具有不同连接率的节点,它们在病毒传播中的作用也不相同,文章还首次给出了它们的估算公式,从而也为刚刚起步的网络免疫系统中节点的选择提供了有力的理论支持。文章最后进行了模拟实验,实验的结果基本验证了分析结论。

Most existing epidemic models for network viruses are rely on epidemic models for biological viruses which are not very accurate to describe the real propagation of the modern viruses,so there are some problems still not be solved properly.Based on a new model,the paper focuses on the two important issues of these problems：the epidemic threshold and the effect of the individual in the virus＂ spreading.By the analysis of the solution to the new model,the paper gets the conclusion that for some viruses,if their spreading depend closely on the connectivity rate of the network and their curing rate are relatively small,then the epidemic thresholds are absent.Thus the paper also gives some proper explanation to the two open problems of the spreading models for network viruses.Taking the connectivity rate as a basic characteristic,the paper points out that different node with different connectivity should has different effect in the virus＇ spreading.For the first time,the paper presents the numerical formula for the effect,which supplies stronger theoretic support for the node＇s selection in the immunization system for modern network virus.Finally,the paper carries out the simulation test and finds the simulation results confirm our analytic results.