基于接触网络的结核病传播动力学研究

The mass level of TB transmission is the dynamic process in social contact networks, therefore it is affected by the structure of the contact network, the transmission mechanism of tuberculosis and environmental factors, which means it is clustering and seasonal. However, most of the existing models ignore these factors, which lead to big errors in the prediction, evaluation and control. This project establishes several types of specific contact network tuberculosis dynamics models which considering the behavior composition of different groups in China.. Theoretically, according to the features of the network model on infectious diseases, we will use the qualitative analysis of the dynamical systems, the theory of the periodic dynamic systems, the theory of nonlinear analysis, complex network theory, center manifold and bifurcation theory to study the transmission threshold values, appearance of bifurcations, and the stability of the equilibrium of tuberculosis network model.. On the application, using the maximum likelihood estimation, the method of least squares, and sensitivity analysis combining with the tuberculosis data in China, we give the range of some key parameters of the prevention and control the spreading of TB in China. In addition, we combined our results with the actual data to analyze and explain the trend of tuberculosis transmission and the problems in prevention and control for tuberculosis.. Our research results will enrich the dynamic of tuberculosis model and enlarge the theoretical results of the dynamic of tuberculosis model. This project is a typical applied and basic research driven by actual problem. The result of this project can provide scientific and quantitative evidence for the public health department to establish relevant policies of preventing and controlling tuberculosis.

群体水平的肺结核传播过程是一个社会接触网络上动力学过程，受接触网络的结构和结核病传播机制及环境因素的影响，具有聚集性和季节性，现有模型大多忽略了这些因素，给预测、评估和控制带来较大误差。本项目将建立几类我国不同群体行为构成的特定接触网络结核病动力学模型。理论上，针对接触网络的特点，利用动力系统定性理论、周期系统动力学理论、非线性分析、复杂网络、中心流形和分支等技巧，研究模型的传播阈值、分支、稳定性。应用上，利用极大似然估计、最小二乘、敏感性分析等方法，结合我国肺结核数据，给出影响我国结核传播、预防和控制的一些关键因素，结合实际数据对不同区域的肺结核传播的流行趋势进行评估和预测，给出防控的优化策略。我们的研究结果将充实结核病动力学模型的研究内容，丰富结核病动力学模型研究的理论结果，属于典型的问题驱动的应用基础研究，得到的主要结论能为公共卫生部门制定相关的防控策略提供科学、定量依据。

肺结核是由结核杆菌感染人体肺部而引发的慢性呼吸道传染病。时至今日仍是我国面临的重大公共卫生问题，严重威胁人民的健康。肺结核的传播过程是一个社会接触网络上的动力学过程，受网络结构、传播机制及环境因素的影响，具有明显的聚集性、季节性、年龄结构等特点。本项目主要研究了几类结核病动力学模型，包括具有年龄结构和时滞效应的结核病模型、具有人口动态演化的网络结核病模型、以及防控干预措施加强对于疾病传播的影响。通过严格的理论分析，我们证明了年龄结构和时滞会导致SEIRS结核病模型发生周期振荡现象，分析了具有人口动态演化的网络结核病模型平衡点的存在性和稳定性、模型的基本再生数、最终规模等；研究了防控干预措施加强引起的传染率下降导致传染病模型发生全局Hopf分支现象，包括分支的稳定性和方向。我们的研究结果将充实结核病动力学模型的研究内容，丰富结核病动力学模型研究的理论结果，属于典型的问题驱动的应用基础研究，得到的主要结论能为公共卫生部门制定相关的防控策略提供科学、定量依据。