登革热病毒感染和振荡传播的数学建模与研究

Dengue fever is a mosquito-borne disease caused by the dengue viruses (DENV), which are transmitted to human by the bite of Aedes female mosquitoes. Significant outbreaks of dengue fever occur from time to time in mainland China and mainly subtropical and tropical regions in the world. Currently, the effective vaccine, which has been developed to prevent the transmission of DENV, is still not available. And it can not be fully understood that the dynamical behavior of virus infection within host and the diseases oscillating transmission between individuals. In the presented project, by applying the theory of dynamical system and numerical simulations, we study the mechanisms of the infection, spread and oscillating transmission of DENV by establishing the dynamical models of infection within host and transmission between human population. Firstly, according to the effect of the neutralizing antibodies and the virus-immunity complexes on DENV infection within host, by means of viral dynamics and immune dynamics, we will propose some dynamical models of DENV infection with-host to explore the mechanism of DENV infection causing severe dengue fever. Secondly, based on the characteristics of multi-strain infection and the role of antibody dependent enhancement for infection and the effect of climatic and environmental change on the diapauses of Aedes eggs and the maintenance of dengue viruses in nature, a series of DENV transmission dynamical models are proposed and investigated to explore the mechanisms leading to the oscillations of the disease transmission. Finally, by analyzing the interdependence between the infection within host and spread among individuals of DENV, we will formulate a series of dengue immuno-epidemiology dynamical models to understand the effect of change of antibody levels in the body on the disease spread among individuals. The obtained results will provide the novel theoretical foundation and guidance for controlling the spread of DENV infection.

登革热是由伊蚊传播登革病毒(DENV)引起的一种蚊媒传播疾病，在我国乃至世界时有发生。目前不仅缺乏有效疫苗，而且在个体内病毒感染和人群间振荡传播的规律仍未充分理解。本项目拟通过建立DENV在个体内感染和群体间疾病传播的动力学模型，综合运用微分动力系统理论、数值模拟等方法，来研究DENV感染和振荡传播的动力学行为。首先，依据DENV感染个体过程中抗体和免疫复合物的作用，借助病毒动力学和免疫动力学的方法，建立DENV感染动力学模型，以探讨其引起重症的原因；其次，根据DENV传播过程中不同毒株的感染特性和抗体增强效应以及气候环境的变化对蚊卵滞育、病毒贮存等影响，建立DENV传播动力学模型，探寻引起DENV振荡传播现象的形成原因；最后基于DENV个体内感染与群体传播的相互依赖性，建立登革热免疫-传染病动力学模型，分析体内抗体变化对疾病传播的影响。研究成果为控制DENV感染和传播提供新的理论基础和依据。

本项目依据登革热体内感染和群体间传播特点，从微观水平体内感染、宏观水平群体间传播以及微观与宏观相结合等方面，建立了若干登革热感染和传播的数学模型，综合运用和发展了传染病动力学、非线性动力系统理论、算子半群理论和数值模拟等方法，阐明了登革热感染后引起重症和疾病传播发生振荡现象的原因。具体来说，(1)基于登革热多菌株感染和抗体依赖增强机制等特点，建立了若干登革热感染动力学模型，确定了模型的基本再生数表达式，研究了侵入平衡态和占优平衡态的存在性、稳定性等，探讨毒株的交叉感染和ADE机制对登革热重症的影响。辨识了系统关键参数的敏感性，给出了登革热毒株初次感染和再次感染的阈值条件，为登革热控制提供了新的思路。(2)根据气候环境变化和转基因不育蚊群释放策略，提出了若干控制登革热传播动力学模型，研究系统的阈值动力学行为，结合数据和数值模拟等方法，甑别了影响登革热传播过程振荡一些主要因素，并给出了最优化控制策略。(3)根据登革热病毒体内感染和群体间传播关联性，建立登革热免疫-传染病动力学模型，给出模型基本再生数表达式，研究系统复杂的动力学行为，快尺度和慢尺度模型的基本再生数之间内在联系，体内病毒感染和免疫变化对登革热病毒传播的动力学影响，确定影响登革热病毒振荡传播的关键性参数，进一步地解释登革热传播过程中振荡现象形成的原因。(4)本项目还对霍乱、疟疾、新冠等进行建模与分析，得到有价值的结果。总之，本项目建立并研究了若干登革热感染和传播的新模型，发展了新的研究方法，其成果可为控制登革热感染和传播提供新的理论基础和依据。项目完成了拟定的研究内容，实现了研究目标。

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