有向网络上流行病阈值比较和免疫分析

Comparison of Epidemic Thresholds on Directed Networks and Immunization Analysis

考虑在有向网络中的流行病阈值以及免疫措施分析的问题,利用SIS模型详细研究了有向网络上的传染病动力学行为。首先获得了一个依赖于有向网络的出度与入度分布和传染力函数的流行病阈值,接着给出了技术网络和社会网络上的流行病阈值表达式。进一步发现当传染力是一个常数时,有向网络中具有较大出度的网络类型更利于疾病传播;而当传染力与网络的出度成正比时,疾病在这两种类型的网络中的传播阈值是相同的。最后通过计算和比较3种在不同的免疫措施下有向网络的流行病阈值,得出了目标免疫明显优于随机免疫和熟人免疫,而随机免疫和熟人免疫的有效性则依赖于网络的入度分布的结论。

We consider the problem of epidemic threshold and immunization strategies analysis in directed networks. In this paper, we investigate and analyse the epidemic dynamics on directed networks via an SIS model. First, we give a general expression of the epidemic threshold, which depends on the in-degree and out-degree distributions of the directed network, and the infectivity function. We figure out the epidemic thresholds on technological and social networks. We find that if the infectivity is a constant, the network with larger average out-degree is more conducive to the spread of diseases, and if the infectivity is proportional to node＇s out-degree, diseases have the same chance to spread in these two kinds of networks. At last, we compute the epidemic thresholds on directed networks with three different immunization schemes. By comparison, we find that targeted immunization has clear superiority to proportional and acquaintance immuniza- tions, and the validity of proportional and acquaintance immunizations relies on the in-degree dis- tribution of networks.