个体异质的半有向渗流耦合网络传染病传播动力学研究

The spread of infectious diseases with the permanent immunity is isomorphic to a bond percolation process. By the method of probability generation function, the epidemic threshold, the probability of an epidemic and the final epidemic size are obtained, moreover, the average outbreak size and the distribution of outbreak sizes below the threshold can be obtained. However, considered only heterogeneous infectivity while neglected heterogeneous susceptibility, the bond percolation model in the present articles fails to predict the correct outbreak size distribution and overestimates the epidemic size and the epidemic probability. Thus, in this project, combining the network topology structure with the specific coupling relationships and heterogeneous infectivity and susceptibility, the spread of infectious diseases with the permanent immunity in a single network is isomorphic to a semi-directed epidemic percolation network. Furthermore, a coupled epidemic percolation network is build. Applying the probability generation function and other mathematical tools, we study the degree distribution of the coupled epidemic percolation network, the average outbreak size and the distribution of outbreak sizes below the threshold, the probability of an epidemic and the final epidemic size. By these above analysis, we can find the influence of individual heterogeneity on the transmission of infectious diseases. These researches make up for the deficiency of the existing studying about the transmission of infectious diseases on the coupled network, and provide theoretical foundation for the prevention and control of infectious diseases.

具有永久免疫的传染病传播可看作沿随机网络上的边渗流过程，借助生成函数理论不仅可获得传染病的流行阈值、流行概率和流行的最终规模，而且还可得到流行阈值之下（即传染病没有流行）爆发规模及其分布。现有成果主要集中在染病节点具有异质性的单个网络上的传染病传播，忽略了易感者的异质性和网络的耦合，高估了传染病流行规模和流行概率，也不能准确预测流行前的规模分布。为此，本项目将结合耦合网络的拓扑结构，考虑网络中个体传染性和易感性的异质性，将单层网络上具有永久免疫的传染病模型同构于一个半有向的渗流网络。利用概率生成函数等工具，研究半有向的渗流耦合网络的度分布、传染病的流行概率、爆发规模及其分布和最终的流行规模，分析个体异质性，特别是易感者的异质性对传染病传播的影响。该研究可弥补传染病渗流理论存在的不足，丰富传染病动力学的研究方法，为传染病的防控提供理论支撑。

具有永久免疫的传染病传播可看作沿随机网络上的边渗流过程，借助生成函数理论不仅可获得传染病的流行阈值、流行概率和流行的最终规模，而且还可得到流行阈值之下（即传染病没有流行）爆发规模及其分布。现有成果主要集中在染病节点具有异质性的单个网络上的传染病传播，忽略了易感者的异质性和网络的耦合，高估了传染病流行规模和流行概率，也不能准确预测流行前的规模分布。为此，本项目将结合耦合网络的拓扑结构，考虑网络中个体传染性和易感性的异质性，将单层网络上具有永久免疫的传染病模型同构于一个半有向的渗流网络。利用概率生成函数等工具，研究半有向的渗流耦合网络的度分布、传染病的流行概率、爆发规模及其分布和最终的流行规模，分析个体异质性，特别是易感者的异质性对传染病传播的影响。该研究可弥补传染病渗流理论存在的不足，丰富传染病动力学的研究方法，为传染病的防控提供理论支撑。