带有时滞的非局部扩散传染病模型波前解的存在性  

Existence of Traveling Wave Fronts of a Nonlocal Dispersal Epidemic Model with Delays

作　　者：姚美萍[1] 李晓霞 赵爱民[1] YAO Meiping;LI Xiaoxia;ZHAO Aimin(School of Mathematical Sciences,Shanxi University Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2022年第2期356-362,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11501339)。

摘　　要：文章主要研究一类带有时滞的非局部扩散传染病模型的波前解问题。利用该系统的特殊结构,将系统波前解的存在性问题转化为一个标量方程的波前解存在性问题,并利用上、下解方法及Schauder不动点定理给出这个标量方程波前解存在的一般性定理。通过构造一对具体的上、下解,证明了当c≥c*时,该标量方程存在波前解,从而得到系统存在波前解。This paper is concerned with the existence of the traveling wave fronts of a nonlocal dispersal epidemic model with delays.We transform the system into the equivalent scalar equation due to the special structure of the system,and we establish a general existence theorem of traveling wave fronts of the corresponding scalar equation via the upper-lower solutions method and Schauder fixed-point theorem.Moreover,by constructing a pair of upper and lower solutions of the corresponding scalar equation,we proved the existence of the traveling wave fronts for c≥c;,which implies the existence of the traveling wave fronts of the system.

关 键 词：非局部扩散系统 波前解 SCHAUDER不动点定理 

分 类 号：O175.1[理学—数学]