本文選題：SEIR模型　切入點：非局部擴散　出處：《蘭州大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：非局部算子相交Laplace算子而言,能夠更精確地刻畫遠距離擴散,越來越多的非局部擴散模型被用于模擬傳染病的擴散.由于行波解可以較好的描述疾病的傳播過程,近年來,非局部擴散傳染病模型行波解的研究得到了廣泛的關(guān)注.本文考慮了兩類擴散SEIR傳染病模型的行波解問題.首先研究了除感染者的擴散為局部擴散外其它的擴散均為非局部的SEIR模型.非局部擴散算子自身緊性與正則性缺失,給我們的研究帶來許多本質(zhì)問題.本文采用截斷的方法來證明行波解的存在性.首先在一足夠大的有界區(qū)域上構(gòu)造一閉錐,用Schauder不動點定理證明了基本再生數(shù)R_01時,在該閉錐上滿足一定初值的行波解的存在性,然后將有界區(qū)域延拓到全空間.用雙邊Laplace變換法證明了當(dāng)基本再生數(shù)R_0≤1時行波解的不存在性.特別地,我們討論了臨界波速時行波解的存在性以及漸近行為.然后考慮了帶有標(biāo)準(zhǔn)發(fā)生率的非局部擴散SEIR傳染病模型的行波解問題.用特征向量法結(jié)合Schauder不動點定理得到行波解的存在性,在證明行波解的不存在性之前,特別給出Laplace變換所需指數(shù)衰減估計的證明.
[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，

本文編號：1601712