非局部扩散SIR及SIRI传染病模型的行波解

兰州大学机构库 >数学与统计学院

	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 Citation GB/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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