Traveling waves in nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay

Advances in Difference Equations

article

Wu, Weixin¹  Teng, Zhidong¹ 

[1] College of Mathematics and Systems Science, Xinjiang University

关键词: Nonlocal dispersal epidemic model;    Nonlinear incidence;    Distributed latent delay;    Traveling waves;    Upper-lower solutions;    Limiting argument;   

DOI  :  10.1186/s13662-020-03073-2

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This paper studies the traveling waves in a nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay. It is found that the traveling waves connecting the disease-free equilibrium with endemic equilibrium are determined by the basic reproduction number$\mathcal{R}_{0}$ and the minimal wave speed$c^{*}$ . When$\mathcal{R}_{0}>1$ and$c>c^{*}$ , the existence of traveling waves is established by using the upper-lower solutions, auxiliary system, constructing the solution map, and then the fixed point theorem, limiting argument, diagonal extraction method, and Lyapunov functions. When$\mathcal{R}_{0}>1$ and$0< c< c^{*}$ , the nonexistence result is also obtained by using the reduction to absurdity and the theory of asymptotic spreading.

【 授权许可】

CC BY