莱姆病传播动力学研究

Lyme disease, the most prevalent tick-borne disease, poses real problems to human health including a number of morbidity and mortality risks. In this project, we will investigate the temporal and spatial dynamics of disease transmission by developing four mathematical models: (1) The first model will describe the transmission of the Lyme pathogen between tick vectors and their host community with various hosts, which gives rise to a high-order ordinary differential system; (2) The second model will describe the disease transmission on spatial scale by considering the tick movement with its host, which is a reaction-diffusion system; (3) The third model will incorporate the temperature effects into Lyme transmission, which will be a reaction-diffusion system with periodic coefficients; (4) The forth one will extend the third model by considering the tick movements with the migratory birds, which will be a reaction-diffusion system with time delay. All these models will be analyzed rigorously by using theories from differential equations, dynamical systems and functional analysis. First, the basic reproduction number for each model will be derived and numerically computed. Then, we will investigate the disease persistence by using the basic reproduction number as the key index. The travelling wave solutions and spreading speeds will be investigated for reaction-diffusion systems. Furthermore, the models will be parameterized with data collected from literature, experiments and surveillance. Numerical simulations will be carried out to determine the mechanisms of spatial spread of the pathogen. Moreover, sensitivity analysis will be implemented to evaluate the cost-effectiveness of control strategies and highlight the most efficient measures.

莱姆病（Lyme disease）是以硬蜱为传播媒介的人畜共患传染病，对人类危害相当严重。为研究疾病的时空传播规律以及预测流行趋势，本项目将建立四个不同的模型：（1）模型一（高维常微分系统）将描述病原体在蜱虫和宿主群落之间的传播；（2）模型二（反应扩散系统）将考虑蜱虫的移动，以此刻画疾病在空间结构上的传播；（3）模型三（周期反应扩散系统）将考虑温度对疾病传播的影响；（4）模型四（具有时滞的反应扩散系统）将研究候鸟迁徙所导致的蜱的移动对疾病传播的影响。 利用微分方程、动力系统和泛函分析理论对这些模型进行严谨的理论分析。首先，定义每个模型的基本再生数，确定基本再生数与疾病的消亡和爆发的关系。对于反应扩散系统，研究行波解的存在性及传播速度。然后，利用文献和实验数据估计参数并对模型进行数值模拟，定量地分析疾病的传播行为。最后，对各参数作敏感性分析。通过敏感性分析得到疾病控制的最优化策略。

莱姆病（Lyme disease）是以硬蜱为传播媒介的人畜共患传染病，对人类危害相当严重。为研究疾病的时空传播规律以及预测流行趋势，本项目将建立四个不同的模型：（1）模型一（高维常微分系统）将描述病原体在蜱虫和宿主群落之间的传播；（2）模型二（反应扩散系统）将考虑蜱虫的移动，以此刻画疾病在空间结构上的传播；（3）模型三（周期反应扩散系统）将考虑温度对疾病传播的影响；（4）模型四（具有时滞的反应扩散系统）将研究候鸟迁徙所导致的蜱的移动对疾病传播的影响。. 利用微分方程、动力系统和泛函分析理论对这些模型进行严谨的理论分析。首先，定义每个模型的基本再生数，确定基本再生数与疾病的消亡和爆发的关系。对于反应扩散系统，研究行波解的存在性及传播速度。然后，利用文献和实验数据估计参数并对模型进行数值模拟，定量地分析疾病的传播行为。最后，对各参数作敏感性分析。通过敏感性分析得到疾病控制的最优化策略。