Complex Systems Research Center, Shanxi University, Taiyuan 030006, China; Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease, Control and Prevention, Shanxi University, Taiyuan 030006, China.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, China; Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease, Control and Prevention, Shanxi University, Taiyuan 030006, China.
J Theor Biol. 2018 Jul 14;449:1-13. doi: 10.1016/j.jtbi.2018.04.007. Epub 2018 Apr 10.
In this paper, the correlation coefficients between nodes in states are used as dynamic variables, and we construct SIR epidemic dynamic models with correlation coefficients by using the pair approximation method in static networks and dynamic networks, respectively. Considering the clustering coefficient of the network, we analytically investigate the existence and the local asymptotic stability of each equilibrium of these models and derive threshold values for the prevalence of diseases. Additionally, we obtain two equivalent epidemic thresholds in dynamic networks, which are compared with the results of the mean field equations.
在本文中，我们将状态节点之间的相关系数作为动态变量，分别利用静态网络和动态网络中的配对近似方法构建了带有相关系数的 SIR 传染病动力学模型。考虑到网络的聚类系数，我们分析研究了这些模型的各个平衡点的存在性和局部渐近稳定性，并推导出了疾病流行的阈值。此外，我们还得到了动态网络中两个等价的传染病阈值，并与平均场方程的结果进行了比较。
