甲型H1N1流感等新发人畜共患传染病的数学建模及动力学研究

项目名称： 甲型H1N1流感等新发人畜共患传染病的数学建模及动力学研究

项目编号： No.11201277

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 张仲华

作者单位： 陕西师范大学

项目金额： 22万元

中文摘要： 全球环境的恶化为病毒变异创造了条件。新病毒使甲型H1N1流感等人畜共患传染病不断暴发并流行，给人类带来极大的威胁。本项目根据疾病的统计数据及传播规律，考虑交通工具对疾病传播的影响，建立疾病在单个封闭斑块内人畜间传播的常微分方程模型、时滞和非自治微分方程模型及在有限个或无穷个斑块间传播的多斑块模型。并运用微分方程理论及泛函分析理论等讨论模型解的适定性等问题。基本再生数是传染病动力学和疾病控制的一个重要的量，在公共卫生及传染病动力学中具有重要的理论和现实意义。但一般的时滞、非自治和多斑块模型的基本再生数还没有明确的计算方法，关于这方面的研究在理论和应用上有待深入。本项目另一个目标是研究基本再生数的理论计算公式及计算方法，给出并分析所建立模型的基本再生数，确定关键因素并优化防治措施。项目的研究将丰富传染病动力学理论及方法，为控制传染病发生发展的时空传播提供理论依据，具有重要的理论和应用价值。

中文关键词： 基本再生数；多斑块模型；稳定性；分歧；

英文摘要： The devastation of the global environment brings convenience to the mutation of many viruses. The newly mutated viruses cause constantly outbreak and spread of anthropozoonosis including influenza A H1N1 and threat the world seriously. According to the statistical data and spreading law of these kinds of diseases, we firstly formulates ordinary differential equation models, time delay differential equation models, non-autonomous differential equation models, and patchy models with finite number or infinite number of patches. Then, the qualitative properties including the well-definedness of solution are respectively discussed by the theory of differential equations and the theory of functional analysis (linear or nonlinear), et al. Basic reproduction number as an important quantity in epidemic dynamics and disease control has importantly theoretical and practical significance in public health and epidemic dynamics. However, there does not exist a clearly method to compute the basic reproductive number of general delay model，non-autonomous model and patchy model with finite number or infinite number of patches, and it is necessary to pay more attention to the computation of the basic reproductive number in both theory and application. As another aim of this project, we investigate the theoretical formulae and com

英文关键词： Basic reproductive number；multi-patch model；stability；bifurcation；