两类非局部扩散SIR传染病模型的行波解 Alternative Title Travelling Waves of Two Kinds of Nonlocal Dispersal SIR Epidemic Models 李燕 Thesis Advisor 李万同 2012-05-27 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 行波解 传染病模型 Holling-II 型发生率 时滞 非局部扩散 常数外部输入 渐近传播速度 Abstract 本文主要考虑了具有全局扩散效应的两类SIR传染病模型行波解的存在性与非存在性. 文章正文由三章组成. 第一章主要介绍了相关问题的背景. 首先说明研究传染病的意义, 然后介绍了传染病模型及其研究状况, 在此基础上提出了本文要研究的问题, 并简要介绍了文章的主要结果和方法. 第二章研究了一个非局部扩散SIR传染病模型的行波解的存在性与非存在性. 得到行波解存在与否决定于基本再生数. 为证非平凡行波解的存在性, 我们在有界区域上构造了一个初始函数的不变锥, 用\ Schauder 不动点定理得到该不变锥上存在不动点, 再通过极限过程得到全空间上存在行波解. 然后用双边Laplace变换证明了当波速小于临界波速时不存在行波解. 最后讨论了空间非局部性对渐近传播速度的影响. 第三章同样在有界区间上构造不变锥证明该锥上存在不动点, 再通过取极限的方法, 研究了一类具Holling-II 型发生率和常数外部输入的时滞非局部扩散SIR传染病模型的行波解的存在性与非存在性, 并讨论了时滞及空间非局部性对渐近传播速度的影响. Other Abstract In this thesis, we consider the existence and nonexistence of traveling wave solutions of two kinds of nonlocal dispersal SIR epidemic model. The main result is divided into two chapters. In the second chapter, we consider a nonlocal dispersal SIR epidemic model. We find that the existence and nonexistence of traveling wave solutions are determined by the reproduction number. To prove the existence of non-trivial traveling wave solutions, we construct an invariant cone in a bounded domain with initial functions being defined on, and apply Schauder's fixed point theorem on this cone, then pass to the unbounded domain by a limiting argument. By means of the two-sided Laplace transform, the nonexistence of traveling wave solutions is obtained as the speed is less than the critical velocity. In the third chapter, we use the same method as the second chapter to study the existence and nonexistence of traveling wave solutions of a delayed nonlocal dispersal SIR epidemic model with constant external suplies and Holling-II incidence rate. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224904 Collection 数学与统计学院 Recommended CitationGB/T 7714 李燕. 两类非局部扩散SIR传染病模型的行波解[D]. 兰州. 兰州大学,2012.
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