新发呼吸道传染病预防控制的动力学模型研究

The implementing effect of prevention and control measures and their intensity during the new outbreak of respiratory infectious disease are often dependent on the disease infection (e.g. number ofreported infected individuals) as well as the volatility ofinfection. Suchdynamic switching threshold policy induces that the epidemiological models which depict the prevention and control strategies occurs discontinuityor non-smooth. It is a completely new research project by employing Filippov systems to describe the dynamic effect andeffectiveness of interventions. The purpose of this project is to formulate the novel Filippov non-smooth epidemiological models with the controlof threshold to study the asymptoticalproperties of solutions of the proposed Filippov systems, to develop the method ofcalculation of the basic reproduction number, to reveal the switching rules of differential equation for the non-smooth systems, and to clarify the similaritiesand differences between the Filippov non-smooth systems and the conventionalsmooth systems. Combining thecomprehensive disease data, statistical reported case data andsensitivity analyses we investigate the dynamic effectiveness of the interventionstrategies during the various stages of disease outbreak. We develop the method ofparameter estimation for the Filippov non-smooth systems and the solving methodfor the optimal control problem for the non-smooth systems, and examineeffectiveness of possible interventions,so as to obtain theoptimal and dynamic threshold policies for infectious disease control. Finally, werealize the quick predication and earlywarning for the new outbreak of respiratory infectious diseases, and effectively curb the respiratory infectious diseases in China, and hence we suggest the optimal scheme forallocation of the limited medical resources and then provide the quantitativebasis for decision-making for the public health sectors.

新发呼吸道传染病暴发过程中，综合防治措施实施效果及其强度依赖于疫情（如报告病例数或治疗的病例数）以及疫情的波动情况，这种动态切换的阈值控制策略导致刻画防控策略的动力学模型存在不连续性或不光滑性。用Filippov系统刻画防控措施实施的动态效果和时效性在传染病动力学中是一个全新的研究课题。本项目旨在建立Filippov非光滑阈值控制的动力学模型，重点研究Filippov系统解的渐近性质，提出该模型基本再生数的计算方法，揭示非光滑系统的微分方程切换规律，阐明非光滑动力系统与传统的连续且光滑系统的异同。结合疾病综合监测、统计报告数据以及敏感性分析探明防治措施在疾病疫情不同阶段的动态效应。发展非光滑动力系统的参数估计方法和最优控制问题的求解方法，研究防治措施的时效性，设计最优的传染病动态阈值控制策略。实现对新发呼吸道传染病的快速预测预警和有效遏制，为公共卫生部门优化资源配置提供理论依据。

新发呼吸道传染病暴发过程中，综合防治措施实施效果及其强度依赖于疫情（如报告病例数或治疗的病例数）以及疫情的波动情况，这种动态切换的阈值控制策略导致刻画防控策略的动力学模型存在不连续性或不光滑性。用Filippov系统刻画防控措施实施的动态效果和时效性在传染病动力学中是一个全新的研究课题。本项目建立了Filippov非光滑阈值控制的动力学模型，重点研究Filippov系统解的渐近性质，提出该模型基本再生数的计算方法，揭示非光滑系统的微分方程切换规律，阐明非光滑动力系统与传统的连续且光滑系统的异同。结合疾病综合监测、统计报告数据以及敏感性分析探明防治措施在疾病疫情不同阶段的动态效应。发展非光滑动力系统的参数估计方法和最优控制问题的求解方法，研究防治措施的时效性，设计最优的传染病动态阈值控制策略。实现对新发呼吸道传染病的快速预测预警和有效遏制，为公共卫生部门优化资源配置提供理论依据。