基于动力学建模的突发传染病应急预案优化配置

There have been many literatures to study the prevalent, duration and forecast the development trend for sudden epidemic diseases.using dynamics method. However，no one applied dynamical theory to study early risk assessment on disease outbreaks, optimal allocation of resources involved in the prevention and control plan and the optimal control strategy. For this reason, in the project, we will build epidemic dynamical model according to the etiology of specific diseases and epidemiological mechanism where it is considered health care resources, such as medical equipment, the number of medical personnel, hospital capacity and the early control strategy (including the isolation and effective vaccine) and other factors during disease outbreak early. Furthermore, analyze risk factors and evaluate quantitatively, study impact on different medical resource constraints for the prevalence of disease. The impact includes waiting for treatment time, the number of infected and death in the process, the final scale of disease, the peak arriving time and assessment of the effectiveness of various control strategies. Then the threshold value, the conditions of stability and bifurcation and other dynamical phenomena will be analyzed. Furthermore, Using the optimization theory a program of optimal allocation of resources and the optimal control strategy will be given. These results or methods are used in SARS and prove feasibility by real data. The research results provide a new theory and methods for the epidemic model.

利用动力学方法对突发传染病流行规模、持续时间、预测发展趋势等的研究已有大量工作，但对疾病爆发早期风险评估、防治预案中涉及的资源优化配置和最优控制策略，利用动力学方法进行研究还未见到。为此，本项目考虑疾病爆发早期涉及的医疗资源，如医疗设备、医务人员数量、医院的容纳量，以及早期的控制策略（包括隔离、有效的疫苗）等因素，根据具体疾病的病原学与流行病学机理建立传染病动力学模型，分析风险因素并对其进行定量评估；研究不同医疗资源制约条件对疾病流行的影响，包括病人等待治疗时间以及期间造成的传染和死亡，对疾病最终规模、高峰到达时间影响，以及各种控制策略的有效性评估；研究模型的阈值、稳定性及分支等动力学现象，结合最优化理论，给出资源优化配置方案及最优控制策略。将所得结果或者方法应用于SARS中，利用实证数据进行验证。该研究成果将为传染病动力学模型提供新的理论和方法。

本项目主要针对医疗资源以及早期的控制策略等因素，根据具体疾病的病原学与流行病学机理建立传染病动力学模型，分析突发传染病的传播过程为背景的传染病传播机理。得到模型的基本再生数及地方病平衡点的存在性及稳定性，发现考虑医疗资源的动力学模型与经典的动力学模型比较，系统发生丰富的动力学性态，包括基本再生数不再是阈值参数即系统经历后向分支、另外系统还经历鞍结点分支、Hopf分支、Bogdanov-Takens分支等性态，并进行仿真，预测了疾病的流行规律和发展趋势，分析疾病流行的原因和关键因素，并且可以得到医疗资源比如病床数的阈值，给出资源优化配置方案及最优控制策略。将所得结果或者方法应用于SARS 中，利用实证数据进行了验证。其结果为传染病模型的研究提供了新的理论和方法，对传染病的防治具有重要指导作用。