传染病染病区域的扩张特征研究

项目名称： 传染病染病区域的扩张特征研究

项目编号： No.11501494

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 张群英

作者单位： 扬州大学

项目金额： 18万元

中文摘要： 禽流感、埃博拉等病毒的传播不仅影响经济的发展，而且严重威胁着人类的健康和安全。数学上，通过建立合理的传染病模型，利用相应的自由边界问题描述病毒的扩散与蔓延，并对其进行理论分析和数值模拟，是数学工作者目前比较紧迫的研究工作之一。本项目拟从动力学角度，以传染病模型为主要研究对象，综合非线性分析、偏微分方程和数值计算等学科的理论为基本工具，重点围绕疾病传播区域的扩张特征进行研究，侧重研究非自治（包括周期）、非均质区域、移动边界等情形下的反应扩散方程组。首先探讨模型解的定性性质和动力学行为，建立与时间、区域特征等因素有关的基本再生数的计算公式，并给出疾病流行与灭绝的判别准则。其次，在理论分析的基础上给出数值模拟结果，并分析传染病病毒扩散与蔓延的一些关键影响因素。. 本项目试图改进和发展现有的一些研究思路和方法，取得更多有价值和新意的研究结果，探索对传染病进行预防和控制的最优策略。

中文关键词： 传染病模型；基本再生数；蔓延与消退；自由边界

英文摘要： The spreading of disease, such as avian influenza, Ebola virus not only influences the development of economy, but also threatens seriously human health and safety. Mathematically, it is one of important work for mathematical researchers to carry on theoretical analysis and numerical simulation by establishing appropriate dynamic model of disease, where free boundary problem describes the spreading of disease. The project will be proposed from the kinetic modeling point of view, using epidemic models as the main research object, and using nonlinear analysis, partial differential equation and numerical simulation as basic tools. We will mostly focus on the spreading feature of epidemic area. Specifically, we will consider some reaction-diffusion systems, involving nonautonomous(including periodic coefficient), heterogeneous environment, moving boundary, etc. Firstly, the qualitative properties and dynamic behaviors of the solutions will be investigated, the formula of the basic reproduction number which related to the time, regional characteristics is to be established. Secondly, the spreading-vanishing dichotomy of disease is explored. Moreover, on the basis of above theoretical analysis, we will give the numerical simulations, and analyze the prevailing reasons and factors of epidemic disease. . The project will try to improve and develop a series of existing research ideas and methods, and get more valuable and new significant results, which are used to explore the optimal strategies for prevention and control of epidemic disease.

英文关键词： Epidemic model;The basic reproduction number;Spreading and vanishing;Free boundary