具有局部结构的增长无标度网络中传染病传播机制研究

Spread dynamics of infectious disease in growing scale-free networks

为了研究人群中的一些基本的社会关系结构,如家庭、室友、同事等,对传染病传播过程的影响机制,本文建立了一个具有局部结构的增长无标度网络模型.研究表明,局部结构的引入使得该网络模型能够同时再现社会网络的两个重要特征:节点度分布的不均匀性以及节点度之间的相关性.首先,该网络的节点度和局部结构度均服从幂律分布,且度分布指数依赖于局部结构的大小.此外,局部结构的存在还导致网络节点度之间具有正相关特性,而这种正相关正是社会网络所特有的一个重要特性.接着,通过理论分析和数值模拟,我们进一步研究了该网络结构对易感者-感染者-易感者(SIS)传染病动力学过程的影响,得到了该传染病系统的临界传播条件及其动力学演化相图,该动力学过程是由局部结构内的局部传播过程和局部结构间的全局传播过程耦合而成,并且同时受到网络拓扑结构和传染病传播机制的影响.所得结果对传染病的防治具有一定的科学指导意义.

Some fundamental social structures in human population, such as household, dormitory, and colleague, are of significant importance for epidemic spreading. In this paper, a growth model of scale-free network incorporating these local structures is introduced, in which both the node degree and the local structure degree follow a power-law distribution with the exponent depending on the size of the local structure. The existence of the local structures also results in the positive correlation between the nodes＇ degree, which is a particularly key feature of social networks. By means of analysis and simulation, we study the effects of network structure on the SIS（susceptible-infected-susceptible） epidemic dynamics, and obtain the epidemic threshold and the phase diagram of prevalence, indicating that the propagation is coupled by the local infection process within local structure and the global infection process between local structures, both of which are governed by the network features and the transmission mechanism. These results are of scientific significance to the control of infectious diseases.