一类带双线性发生率的非局部扩散SI传染病模型的行波解 Alternative Title Wave propagation in a nonlocal dispersal SI epidemic model with bilinear incidence 李嘉敏 Subtype 学士 Thesis Advisor 杨飞英 2021-05-20 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 理学学士 Degree Discipline 应用数学 Keyword SI 传染病模型 非局部扩散 行波解 极小波速 Abstract 本文主要研究一类带双线性发生率的非局部扩散 SI 传染病模型的行波解. 文章首先介绍了传染病问题的研究背景以及研究传染病模型的重要意义, 然后介绍传染病模型及其发展进程, 并在此基础上提出要研究的问题. 本文第二章考虑行波解的存在性及其渐近行为. 在波速大于波速临界值条件下, 利用上下解方法, 再结合 Schauder’s 不动点定理以及常微分方程的相关理论, 证明了行波解的存在.然后结合核函数的相关性质对方程进行分析, 通过推导得出矛盾的方法证明了在波速大于等于波速临界值条件下行波解的渐近行为. 第三章考虑行波解的不存在性. 在波速小于波速临界值的条件下, 通过结合相应非局部方程对应的特征值问题, 以及假设分析得出矛盾, 证明弱行波解的不存在性. Other Abstract In this article we study the traveling wave solutions for a class of nonlocal dispersal SI epidemic model with feedback control. Firstly, we introduce the research background and the importance of studying the infectious disease problem in this paper, and then introduce the infectious disease model and its development process. On this basis, put forward the problems to be studied. The second chapter of this paper considers the existence and asymptotic behavior of traveling wave solutions. When the speed is greater than the critical velocity, to prove the existence of traveling wave, we use the upper and lower solution method and apply the Schauder fifixed point theorem and the related theories of ordinary differential equations. Then, we obtain the asymptotic behavior of the traveling wave solution by the method of proof by contradiction. Chapter 3 considers the non-existence of the traveling wave solution while the speed is less than the critical velocity. A contradiction is obtained through hypothetical analysis to prove that the weak traveling wave solution is not existed. Pages 41 URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/461013 Collection 数学与统计学院 Affiliation 数学与统计学院 First Author Affilication School of Mathematics and Statistics Recommended CitationGB/T 7714 李嘉敏. 一类带双线性发生率的非局部扩散SI传染病模型的行波解[D]. 兰州. 兰州大学,2021.
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