若干蚊子传播疾病的动力学建模与新的控制策略研究

Mosquito-borne diseases, such as malaria, dengue, have been a big challenges to the public health. Researchers have studied the stable transmission dynamics and established strategies in the control of these diseases. However, these studies are still far from their completion due to the complexity of the life cycle of these diseases. To have a better and deeper understanding of the transmission mechanism that are responsible for the oscillations and outbreak dynamics of these diseases, and to suggest new control strategies, we will formulate new mathematical models including dynamics of mosquitoes populations, multi-strains infection, and transgenic mosquitoes in this proposed research. Meanwhile, more challenging mathematical questions raised from these new models will be also investigated.Taking advantage ofthe richer theoretical foundation of the well-developed theory of dynamical systems, nonlinear system control,epidemic dynamics and the available powerful and efficient computational tools, such as Matlab,we will analyze the complex dynamical properties of these models, such as bifurcations,period-doubling solutions,and competitive exclusion and multistrains coexistence. It is expected that new techniques and methods in epidemic dynamical system theory will be applied and developed. We will give more complete qualitative and quantitative analysis for the proposed models, and investigate the reseason of the oscillations and outbreak dynamics borne of these diseases and the impact of releasing transgenic mosquitoes on the disease transmissions.By modeling and mathematical analysis, we will provide a useful guidance for optimal control strategies for possible eradication or significant reduction of the transmission of mosquito-borne diseases to the biological and public health communities. Moreover, the proposed research is expected to have a big impact on education by stimulating more students interested in and recruited into such interdisciplinary research.

疟疾、登革热等蚊子传播疾病已对人们公共健康提出了独特挑战。许多学者建立和研究了这些疾病传播的稳定动力学特征和控制策略，但这还远不能完整地刻画蚊子传播疾病的复杂性。为了探讨引起疟疾震荡、爆发的原因和控制其传播的新策略，本项目拟结合蚊子种群动力学、多菌株感染以及转基因蚊子引入，来构建若干蚊子传播疾病新模型，同时也研究由此可提出的具有挑战性的数学问题。本项目综合地运用现代动力系统、非线性控制和传染病动力学基础理论以及Matlab等有效计算工具,来分析模型中复杂的动力学性质,如各种分支、倍周期解和菌株共存、排斥等。通过该项目研究,我们希望一方面不断地运用和发展传染病动力系统中新技巧和新方法，尽可能完善地定性和定量地研究模型复杂动力学性质，分析引起疾病震荡、爆发的原因和转基因蚊子引入的影响,另一方面为公共管理部门运用最优策略消除蚊子传播疾病提供理论参考依据以及指导和培养研究生对交叉学科的研究兴趣。

疟疾、登革热等蚊子传播疾病已对人们公共健康提出了独特挑战。为探讨引起疟疾震荡爆发的原因和控制其传播的新策略，本项目结合蚊子种群动力学、多菌株感染以及转基因蚊子引入，构建了若干蚊子传播疾病新模型: 蚊子种群动力学耦合传染病动力学模型，多菌株感染的疟疾传播动力学模型，转基因蚊子作用下的疟疾传播动力学模型，以及包含运用和发展传染病动力学中的嵌套理论、方法，建立的免疫--传染病耦合疟疾传播的动力学模型 (这样把人体内疟原虫病毒感染(微观模型)与疟原虫病毒在人和蚊群中传播(宏观模型)联系起来而)等。通过综合地运用现代动力系统、非线性控制和传染病动力学基础理论以及Matlab 等有效计算工具,我们全面地分析模型中复杂的动力学性质,如各种分支、倍周期解和菌株共存、排斥等。通过该项目研究, 我们给出了一些引起疟疾传播震荡的因素，获得了最优控制和预防蚊子传播疾病的新策略. 另外，本项目研究能够为公共管理部门运用最优策略消除蚊子疾病传播提供理论参考依据，以及指导和培养研究生对交叉学科的研究兴趣。研究成果以论文形式发表，共发表论文21篇，其中SCI收录期刊上发表17篇。