一类带有标准发生率的非局部扩散传染病模型的传播现象

发布时间：2018-03-12 13:14

  本文选题：SEIR模型　切入点：非局部扩散　出处：《兰州大学》2017年硕士论文　论文类型：学位论文

【摘要】：非局部算子相交Laplace算子而言,能够更精确地刻画远距离扩散,越来越多的非局部扩散模型被用于模拟传染病的扩散.由于行波解可以较好的描述疾病的传播过程,近年来,非局部扩散传染病模型行波解的研究得到了广泛的关注.本文考虑了两类扩散SEIR传染病模型的行波解问题.首先研究了除感染者的扩散为局部扩散外其它的扩散均为非局部的SEIR模型.非局部扩散算子自身紧性与正则性缺失,给我们的研究带来许多本质问题.本文采用截断的方法来证明行波解的存在性.首先在一足够大的有界区域上构造一闭锥,用Schauder不动点定理证明了基本再生数R_01时,在该闭锥上满足一定初值的行波解的存在性,然后将有界区域延拓到全空间.用双边Laplace变换法证明了当基本再生数R_0≤1时行波解的不存在性.特别地,我们讨论了临界波速时行波解的存在性以及渐近行为.然后考虑了带有标准发生率的非局部扩散SEIR传染病模型的行波解问题.用特征向量法结合Schauder不动点定理得到行波解的存在性,在证明行波解的不存在性之前,特别给出Laplace变换所需指数衰减估计的证明.
[Abstract]:The nonlocal operator intersecting Laplace operator can describe long distance diffusion more and more accurately. More and more nonlocal diffusion models are used to simulate the spread of infectious diseases. Because traveling wave solutions can better describe the spread process of disease, in recent years, more and more nonlocal diffusion models can be used to simulate the spread of infectious diseases. The study of traveling wave solution of nonlocal diffusive infectious disease model has been paid more and more attention. In this paper, we consider the traveling wave solution of two kinds of diffusive SEIR infectious disease model. The nonlocal diffusion operator lacks compactness and regularity. In this paper, the existence of traveling wave solution is proved by means of truncation. Firstly, a closed cone is constructed on a bounded region which is large enough, and the basic reproducing number R _ S _ 1 is proved by Schauder fixed point theorem. The existence of traveling wave solutions satisfying some initial values on the closed cone is obtained, and then the bounded region is extended to the whole space. The nonexistence of the travelling wave solution for the basic regenerative number R0 鈮，

本文编号：1601712