斑块环境下具有潜伏期的两种群传染病模型的行波解

发布时间：2018-05-08 06:02

  本文选题：两种群传染病 + 斑块环境　； 参考：《兰州大学》2017年硕士论文

【摘要】：本文主要考虑了斑块环境下具有潜伏期的两种群传染病模型的行波解的存在性与不存在性.正文由以下四章组成.第一章首先介绍了本文的背景以及传染病模型发展的概况,其次介绍了本文研究的具体问题和结果,即斑块环境下具有潜伏期的两种群传染病模型的行波解的存在性与不存在性.第二章利用离散的傅里叶变换推导出了斑块环境下具有潜伏期的两种群传染病模型.第三章通过构造适当的上,下解得到一个在全空间区域R上的不变锥,然后利用Schauder不动点定理,证明了当基本再生数R_0(S_1~0,S_0~2)1且波速c大于临界波速(c~*时该系统存在一个非平凡的行波解.最后利用反证法证明了当R_0(S_1~0,S_0~2)≤1,c0时不存在满足ψ_i(±∞)=0,φ_i(-∞)=S_i~0,i=1,2的非平凡的行波解.第四章对本文中尚未解决的问题进行探讨,同时对论文后续的工作以及感兴趣的问题进行了简单的介绍.
[Abstract]:In this paper, we consider the existence and non-existence of traveling wave solutions of two species infectious disease model with latent period in patch environment. The text consists of the following four chapters. The first chapter introduces the background of this paper and the development of infectious disease models, and then introduces the specific problems and results of this study. That is, the existence and non-existence of traveling wave solution of two species infectious disease model with latent period in plaque environment. In chapter 2, a two-species infectious disease model with latent period in plaque environment is derived by discrete Fourier transform. In chapter 3, by constructing appropriate upper and lower solutions, we obtain an invariant cone on the whole space R, and then use the Schauder fixed point theorem. It is proved that the system has a nontrivial traveling wave solution when the basic regenerative number R _ S _ 0 / S _ 1 / S _ S _ 1 / S _ S _ 0 / T _ 1 and the wave velocity _ c is larger than the critical wave velocity ~ ~ ~ *. Finally, it is proved by the method of counter-proof that there is no nontrivial traveling wave solution which satisfies 蠄 _ I (卤鈭，

本文编号：1860248