行为变化、旅途感染及边境检疫对传染病空间传播的影响

Infectious diseases, particularly airborne and direct contact diseases, are a major threat to global health. A total of 1 billion cases of flu, 3-5 million cases of severe illness and 300,000-500,000 deaths were estimated annually. In 2014, there were roughly 9.6 million active tuberculosis cases and 1.5 million deaths. Measles caused 114,900 deaths worldwide in 2014, the vast majority are children under the age of five. The rapid expansion of global transport network facilitates the spread of infectious diseases. This project is devoted to the study of the effects of behavior change, transport-related infection and border screening on the disease persistence, prevalence and distribution, dynamical behavior, and efficacy of control measures in a patchy environment. We are among the first to model behavior-dependent human movement, to correct the double-counting flaw in considering transmission within and between patches, and to explicitly take the duration of travel into consideration. Based on the multipatch SIS (susceptible-infectious-susceptible) epidemic model, we analyze and compare the full and sub-models that incorporate either behavior change, or transport-related infection or border screening. For the same theme, we further generalize the model through inclusion of environmental seasonality and stochasticity and more epidemiological factors to develop a complete mathematical theory. The study has the potential to help public health agencies to implement migration management and passenger quarantine to reduce disease burden and to assess the impact of China's high-speed rail project and urbanization plan on the spread of infectious diseases.

传染病特别是空气传播和直接接触传播疾病是公众健康的一大威胁。每年流感新发病例高达10亿，其中重症患者3~5百万，死亡人数30~50万。2014年，全球新增结核病人960万，死亡150万。同年麻疹死亡人数11万4千9百，多为五岁以下儿童。全球交通网络的快速拓展便利了传染病的传播。本项目研究斑块环境下行为变化、旅途感染、和边境检疫等因素对传染病持续性、患病率和其分布、疾病动力学、和疾控措施效力等的影响。首次建模人口迁移依赖行为变化，纠正旅途感染和在地感染的重复计算缺陷，将旅行时长显示地纳入模型。从SIS斑块模型出发，对考虑行为变化、旅途感染、边境检疫的部分或全部的子模型和主模型逐一分析和比较，进而考虑季节变化或剧烈波动环境、和复杂结构模型，研究同一主题，建立一套完整的数学理论。它对公共卫生部门如何通过迁移调控和旅客检疫以减少疾病危害和评估高铁建设和城镇化规划对传染病传播的影响具有重要价值。

传染病是公众健康的最大威胁之一，每年造成超过七百万人口的死亡。全球化、城市化和交通发展便利了传染病的传播与扩散，并给传染病的控制与消除带来了严峻的挑战。近几十年里，大量传染病数学模型被提出和研究。这些工作在理解传染病传播机理、预测传播趋势和优化控制措施方面发挥重要作用。本项目建立多个数学模型，考虑行为变化、旅途感染和人口流动等因素对传染病传播与控制的影响。主要研究结果包括：（1）提出两个考虑意识项目影响的霍乱模型，得到模型的持久性、灭绝性、地方病平衡点的存在性和稳定性等结果，并对两个模型动力学行为进行了比较。（2）构造新模型以纠正某些现有模型中存在的旅途感染和在地感染重复计算的缺陷，证明旅途感染未必一定导致更多感染。（3）对带有标准发生率的SIS 斑块模型，证明了基本再生数关于染病者扩散系数是严格单调递减和严格凸的，并由此得到一些重要结论和应用。（4）考虑到人们在出行频率上的异质性，建立了一类两组群的SIS斑块模型，推导了模型的基本再生数和估计其上下界，在一定条件下得到全局动力学结果，基于再生数比较传统模型与新模型，分析人口流动变化趋势对传染病传播的影响。（5）基于多斑块Ross-Macdonald模型，证明人和蚊子的非均匀分布会增强疟疾的持久性。该课题的研究有助于我们更好地理解人口流动对传染病传播的影响，指导公共卫生部门通过媒体宣传、迁移干预、与资源配置等非药物手段来减少疾病危害和评估高铁建设与城镇化规划对传染病传播的影响。