DS-DI 传染病模型的行波解 Alternative Title Traveling Waves of DS-DI Epidemic Model 赵琳 Thesis Advisor 王智诚 2013-05-23 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 非平凡行波解 DS-DI传染病模型 双线性发生率 非局部时滞 Abstract 本文主要考虑了DS-DI传染病模型非平凡行波解的存在性与不存在性。 正文由以下两章组成。 第一章介绍了本文的研究背景以及主要结果。 首先, 介绍了传染病对人类健康的危害以及研究传染病具有非常重要的意义。其次,介绍了传染病数学模型的发展概况以及本文所要研究的具体问题和结果,即本文研究一类具有非局部时滞影响的DS-DI模型,建立其非平凡行波解的存在性和不存在性. 第二章证明本文研究的主要结果.当基本再生数R0<下标!>> 1 时, 我们证明了非平凡行波解的存在性。方法是在一个有界域上构造一个不变锥, 然后利用Schauder不动点定理证明该锥上存在一个不动点, 最后通过极限过程将其拓展到全空间R中; 当R0<下标!>< 1 时,利用反证法证明了非平凡行波解的不存在性。 Other Abstract This thesis is concerned with the existence and nonexistence of nontrivial traveling wave solutions of DS-DI epidemic model. The thesis consists of the following two chapters. In chapter 1, we introduce the background of the epidemic and some related knowledge. Firstly, we state the epidemic is harmful to human healthy and it is meaningful for researching the epidemic. Secondly, we introduce the development of the epidemic mathematical model and the main results of the thesis. That is we consider a nonlocal delay DS-DI epidemic model, and find that the existence and nonexistence of traveling wave solutions are determined by the reproduction number R0<下标!>. In chapter 2 , we prove the main results of the thesis . When R0<下标!>>1 , we construct an invariant cone in a bounded domain with initial functions being defined on , and apply a fixed point theorem on this cone , then extend to the unbounded domain R by a limiting argument. When R0<下标!>< 1 , we prove the nonexistence of traveling wave solutions by a contradiction argument. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225717 Collection 数学与统计学院 Recommended CitationGB/T 7714 赵琳. DS-DI 传染病模型的行波解[D]. 兰州. 兰州大学,2013.
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