一类具有非线性发生率与时滞的离散扩散SIR模型临界行波解的存在性

张笑嫣

doi:10.21656/1000-0887.420111

一类具有非线性发生率与时滞的离散扩散SIR模型临界行波解的存在性

doi: 10.21656/1000-0887.420111

张笑嫣^,

西安电子科技大学数学与统计学院，西安 710071

基金项目:

陕西省杰出青年科学基金(2020JC-24)

详细信息

作者简介:
张笑嫣(1997—), 女, 硕士生(E-mail: 979739359@qq.com).

通讯作者:
张笑嫣(1997—), 女, 硕士生(E-mail: 979739359@qq.com).

中图分类号: O357.41
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- 文章访问数: 620
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- 被引次数: 0
出版历程
- 收稿日期: 2021-04-28
- 修回日期: 2021-06-09
- 网络出版日期: 2021-12-31

Existence of Critical Traveling Wave Solutions for a Class of Discrete Diffusion SIR Models With Nonlinear Incidence and Time Delay

ZHANG Xiaoyan^,

School of Mathematics and Statistics, Xidian University, Xi’an 710071, P.R.China

摘要

摘要: 研究了一类具有非线性发生率的离散扩散时滞SIR模型的临界行波解的存在性.在人口总数非恒定的条件下，首先,应用上下解法与Schauder不动点定理证明了解在有限闭区间上的存在性；其次，通过极限讨论了临界行波解在整个实数域上存在;最后，通过反证法与波动引理得到了行波解在无穷远处的渐近行为.
- 离散扩散SIR模型 /
- 行波解 /
- 非线性发生率 /
- 时滞
Abstract: The existence of critical traveling wave solutions for a class of discrete diffusion SIR models with nonlinear incidence and time delay were studied. Under the condition that the total population is not a constant, the upper and lower solutions method and the Schauder fixed point theorem were used to prove the existence of the solution on a finite interval. Furthermore, the existence of critical traveling wave solutions was proved on the real number field through limit arguments. Finally, with the fluctuation lemma and the proof by contradiction, the asymptotic boundary of the critical traveling wave was obtained.
- discrete diffusion SIR model /
- traveling wave solution /
- nonlinear incidence /
- time delay

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参考文献(18)

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