当前位置: X-MOL 学术Math. Methods Appl. Sci. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Traveling waves in a nonlocal delayed epidemic model with diffusion
Mathematical Methods in the Applied Sciences ( IF 2.9 ) Pub Date : 2021-04-30 , DOI: 10.1002/mma.7452
Kun Li 1 , Xiong Li 2
Affiliation  

In this paper, we are concerned with traveling waves in a nonlocal delayed epidemic model with diffusion. Firstly, by considering a six-dimensional nondelayed system with the help of variable transformation, we establish the existence of monotone traveling waves by means of the abstract theory, which implies the existence of traveling waves connecting the disease-free equilibrium and the epidemic coexistence equilibrium. Secondly, we prove the global stability of traveling waves based on spectral analysis method, which reveals that the solutions of the initial values and the traveling waves are exponentially close. Thirdly, we obtain that the wave speed is unique by choosing suitable parameters to construct new upper and lower solutions, which shows that the bistable waves keep the uniqueness of the wave speeds in the case of nonlocal delays. As an application of our results, we give a special example.

中文翻译:

具有扩散的非局部延迟流行病模型中的行波

在本文中,我们关注具有扩散的非局部延迟流行病模型中的行波。首先,通过变量变换考虑一个六维非时滞系统,我们借助抽象理论建立了单调行波的存在性,这意味着连接无病平衡和流行病共存平衡的行波存在. 其次,我们基于谱分析方法证明了行波的全局稳定性,表明初始值与行波的解呈指数接近。第三,我们通过选择合适的参数构建新的上下解得到波速唯一性,这表明双稳态波在非局部延迟的情况下保持了波速的唯一性。
更新日期:2021-04-30
down
wechat
bug