本文選題：兩種群傳染病 + 斑塊環(huán)境��； 參考：《蘭州大學(xué)》2017年碩士論文

【摘要】：本文主要考慮了斑塊環(huán)境下具有潛伏期的兩種群傳染病模型的行波解的存在性與不存在性.正文由以下四章組成.第一章首先介紹了本文的背景以及傳染病模型發(fā)展的概況,其次介紹了本文研究的具體問題和結(jié)果,即斑塊環(huán)境下具有潛伏期的兩種群傳染病模型的行波解的存在性與不存在性.第二章利用離散的傅里葉變換推導(dǎo)出了斑塊環(huán)境下具有潛伏期的兩種群傳染病模型.第三章通過構(gòu)造適當(dāng)?shù)纳?下解得到一個在全空間區(qū)域R上的不變錐,然后利用Schauder不動點定理,證明了當(dāng)基本再生數(shù)R_0(S_1~0,S_0~2)1且波速c大于臨界波速(c~*時該系統(tǒng)存在一個非平凡的行波解.最后利用反證法證明了當(dāng)R_0(S_1~0,S_0~2)≤1,c0時不存在滿足ψ_i(±∞)=0,φ_i(-∞)=S_i~0,i=1,2的非平凡的行波解.第四章對本文中尚未解決的問題進(jìn)行探討,同時對論文后續(xù)的工作以及感興趣的問題進(jìn)行了簡單的介紹.
[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 (鹵鈭，

本文編號：1860248