非局部扩散SIR及SIRI传染病模型的行波解 Alternative Title Traveling waves for nonlocal dispersal SIR and SIRI epidemic models 王佳兵 Thesis Advisor 李万同 2014-05-22 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword SIR 模型 SIRI 模型 非局部扩散 时滞 行波解 Abstract 本文主要研究带非局部时滞的非局部扩散SIR 传染病模型和具有常数外部输入项的非局部扩散SIRI 传染病模型的行波解. 首先介绍了SIR 传染病模型的研究背景、研究进程和本文所得的主要结果. 其次我们考虑了带非局部时滞的非局部扩散SIR 模型. 通过构造有界域上的 不变锥, 利用Leray-Schauder 不动点定理, 利用一个极限过程证明了该模型行波解 的存在性及渐近行为. 使用双边 Laplace 变换证得了波速小于临界波速时行波解的不存在性. 此外还讨论了非局部时滞和空间扩散形式对疾病传播快慢的影响. 最后考虑了带常数外部输入项的非局部扩散SIRI 传染病模型. 该模型适用于 研究具有复发效应的传染病. 我们首先利用Banach 压缩映像原理得到初值问题的 适定性. 进一步借助部分拟单调条件、上下解方法、迭代技术及不动点定理得到连 接两个平衡点行波解存在的充分条件. 最后通过比较原理证得该模型行波解的不存在性. Other Abstract In this thesis, we study mainly the traveling waves for a nonlocal dispersal SIR epidemic model with nonlocal delay and a nonlocal dispersal SIRI epidemic model with constant external suply. First, we introduce the research background and process concerning the SIR epidemic model as well as some main results of this essay. Second, a nonlocal dispersal SIR model with nonlocal delay is established. In order to prove the existence and asymptotic behavior of non-trivial traveling wave solutions, we construct an invariant cone in a bounded domain and apply the fixed point theorem as well as limiting arguments. Furthermore, we show that there does not exist traveling wave solution if the speed is less than the critical velocity. Finally, we consider a nonlocal dispersal SIRI epidemic model with constant external suply. This model can be used to describe some diseases with relapse. Firstly, the well posededness of the model is obtained via the Banach contracting theorem. Then the sufficient conditions for the existence of traveling waves are derived by the partial quasi-monotone condition, the super-lower solutions method and the fixedpoint theorem. Finally the non-existence of traveling wave solutions is proved by the comparison principle. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225471 Collection 数学与统计学院 Recommended CitationGB/T 7714 王佳兵. 非局部扩散SIR及SIRI传染病模型的行波解[D]. 兰州. 兰州大学,2014.
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