一类具有非线性发生率与时滞的非局部扩散SIR模型的行波解

数学物理学报 ›› 2018, Vol. 38 ›› Issue (3): 496-513.

一类具有非线性发生率与时滞的非局部扩散SIR模型的行波解

邹霞, 吴事良

西安电子科技大学数学与统计学院西安 710071

收稿日期:2016-08-31 修回日期:2017-08-26 出版日期:2018-06-26 发布日期:2018-06-26
通讯作者: 吴事良 E-mail:slwu@xidian.edu.cn
作者简介:邹霞,E-mail:770572241@qq.com
基金资助:
国家自然科学基金（11671315）和陕西省自然科学基金（2017JM1003）

Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Delay and Nonlinear Incidence

Zou Xia, Wu Shiliang

School of Mathematics and Statistics, Xidian University, Xi'an 710071

Received:2016-08-31 Revised:2017-08-26 Online:2018-06-26 Published:2018-06-26
Supported by:
Supported by the NSFC (11671315) and the Natural Science Foundation of Shaanxi Province (2017JM1003)

摘要/Abstract

摘要： 该文研究了一类具有非线性发生率与时滞的非局部扩散SIR传染病模型的行波解问题.利用基本再生数R₀和最小波速c^*判定行波解的存在与否.首先，当c>c^*，R₀>1时，通过对一个截断问题使用Schauder不动点定理以及取极限的方法证明了所研究模型的行波解的存在性.其次，当0 < c < c^*，R₀>1或R₀ ≤ 1时，利用双边拉普拉斯变换的性质证明了行波解的不存在性.

关键词: 非局部扩散, 行波解, SIR模型, Schauder不动点定理

Abstract: This paper is concerned with the traveling waves of a nonlocal dispersal SIR epidemic model with delay and nonlinear incidence. The threshold dynamics are determined by the basic reproduction number R₀ and the minimal wave speed c^*. First, when c > c^*, R₀ > 1, the existence of the traveling waves is proved by applying Schauder's fixed point theorem and a limiting argument. Then, when 0 < c < c^*, R₀ > 1 or R₀ ≤ 1, the non-existence of traveling wave solutions is established by two-side Laplace transform.

Key words: Non-local dispersal, Traveling wave solution, SIR model, Schauder's fixed point theorem

中图分类号:

O175.14

邹霞, 吴事良. 一类具有非线性发生率与时滞的非局部扩散SIR模型的行波解[J]. 数学物理学报, 2018, 38(3): 496-513.

Zou Xia, Wu Shiliang. Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Delay and Nonlinear Incidence[J]. Acta mathematica scientia,Series A, 2018, 38(3): 496-513.

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