传染病反应扩散的多层次建模与动力学分析

The transmission of epidemics through vast regions is a complicated reaction-diffusion phenomenon, which is affected by combined factors such as pathogen, human, environment and climate. But existing studies of epidemic dynamics mainly focus on human mobility and direct infection, where the effects of indirect factors are usually overlooked. Here we take into account various related factors (e.g., climatic environment, social economics, floating population and collective behaviors), and consider the dynamic coupling between these factors and disease propagation. We define the framework of multilevel dynamics by integrating indirect factors, infection data and direct transmission, and develop a new type of epidemic reaction-diffusion models in the form of mathematics, statistics and computation. Further, we employ qualitative theory, functional differential equations and statistical regression as well as Bayes inference and MCMC methods to explore various dynamic behaviors including spreading threshold, diffusion routes, incidence rate, periodic oscillations and Turing patterns, so as to infer the mechanisms of spatio-temporal transmission. Particularly, we apply our model to the transmission of tuberculosis and dengue in China. We investigate the contributions of explicit and hidden factors to the transmission, reveal the propagation rules behind the data of reported cases, and develop effective control strategies. Our studies can provide more reasonable methodology for the studies on epidemic dynamics, and can present scientific guidance for the control and intervention of epidemics.

传染病的大范围传播是一种复杂的反应扩散现象，受病原体、人类、环境和气候等多种因素共同影响。但现有传染病动力学研究主要关注人群移动和直接传播，往往忽略了间接因素的作用。本项目综合多种相关因素，如气候环境、社会经济、流动人口和群体行为等，分析它们与传播的耦合作用，提出由间接因素、病例数据和直接感染构成的多层次耦合动力学，由此建立一类新的传染病反应扩散的数学、统计和计算模型；接着运用定性理论、泛函微分、随机理论和统计回归等知识，并结合贝叶斯推断和马氏链蒙特卡罗方法，探索传播阈值、扩散路径、发病率、周期振荡和图灵斑图等各种动力学行为，获得疾病的时空传播机理。并把新模型应用于肺结核和登革热在全国多个地区的真实传播，讨论各种显性和隐性因素的影响权重，揭示病例数据下隐藏的传播规律，给出恰当的控制策略。研究结果将为传染病动力学提供更合理的建模分析方法，并为疫情的预防和控制提供科学指导。

传染病流行是感染源通过各种途径感染易感人群或动物，是一个时空上反应扩散的多层次过程，与气候、经济、交通、人口和环境等一系列因素密切相关，结合影响因素探究各类传染病的暴发、扩散与消亡问题是当前的研究热点。本项目提出了一类嵌入传播因子的传染病多层次建模方案，并应用于分析多种传染病的反应扩散机理。着重研究了如下三类问题：（1）结合疫情数据、气象信息和社会环境等因素，采用动力学模型、ArcGIS、小波分析、统计模型和机器学习等技术，分析了登革热在广东区县、地级市和珠三角多个尺度下的时空演化图、风险分布图、关键路径和传播网络等动力学性质，给出了气象、人口流动和社会经济对疫情时空扩散的影响作用。（2）建立一类传染病模型，耦合了气候条件、社会网络结构、群体接触模式、年龄结构、人口特征等各类影响因素，由此形成反映传染病传播的多层次模型，据此分析手足口病、禽流感、肺结核、HIV、包虫病等多个传染病的反应扩散机理，量化因素的影响权重。（3）把蚊媒防控、接种和市场干预等措施融入传播动力学模型中，分析各类防控措施对登革热、手足口和禽流感时空扩散的影响机制，进而优化疫情的防控措施。. 依托本项目研究，共发表学术论文23篇，其中SCI收录16篇，中文核心4篇。指导和培养青年教师3名、培养硕士12名。研究成果为传染病分析提供建模思路，有助于从本质认识传染病的传播规律和流行特征，从而制订有效的防控措施。