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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- 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)

HOSONO Y, ILYAS B. Traveling waves for a simple diffusive epidemic model[J].Mathematical Models and Methods in Applied Sciences,1995,5(7): 935-966.

[2]BAI Z G, WU S L. Traveling waves in a delayed SIR epidemic model with nonlinear incidence[J].Applied Mathematics and Computation,2015,263: 221-232.

[3]WANG X X, WANG H Y, WU J H. Traveling waves of diffusive predator-prey system: disease outbreak propagation[J].Discrete and Continuous Dynamical Systems（Series A）,2015,32(9): 3303-3324.

[4]WANG H Y, WANG X S. Traveling wave phenomena in a Kermack-McKendrick SIR model[J].Journal of Dynamics and Differential Equations,2016,28: 143-166.

[5]FU S C, GUO J S, WU C C. Traveling wave solutions for a discrete diffusive epidemic model[J].Journal of Nonlinear Science,2016,31(10): 1739-1751.

[6]CHEN Y Y, GUO J S, HAMEL F. Traveling waves for a lattice dynamical system arising in a diffusive endemic model[J].Nonlinearity,2016,30(6): 2334-2359.

[7]WU C C. Existence of traveling waves with the critical speed for a discrete diffusive epidemic model[J].Journal of Differential Equations,2017,262(1): 272-282.

[8]YANG F Y, LI W T. Traveling waves in a nonlocal dispersal SIR model with critical wave speed[J]. Journal of Mathematical Analysis and Applications,2017,458(3): 1131-1146.

[9]SHU H Y, PAN X J, WANG X S, et al. Traveling waves in epidemic models: non-monotone diffusive systems with non-monotone incidence rates[J].Journal of Dynamics and Differential Equations,2018,31: 883-901.

[10]SAN X F, WANG Z C. Traveling waves for a two-group epidemic model with latent period in a patchy environment[J].Journal of Mathematical Analysis and Applications,2019,475(2): 1502-1531.

[11]SAN X F, SUN J W. Spreading speed for an epidemic model with time delay in a patchy environment[J].Proceedings of the American Mathematical Society,2021,149: 739-746.

[12]ZHANG R, WANG J L, LIU S Q. Traveling wave solutions for a class of discrete diffusive SIR epidemic model[J].Journal of Nonlinear Science,2021,31(1): 1-33.

[13]ZHOU J B, SONG L Y, WEI J D. Mixed types of waves in a discrete diffusive epidemic model with nonlinear incidence and time delay[J].Journal of Differential Equations,2020,268(8): 4491-4524.

[14]WEI J D, ZHOU J B, ZHEN Z L, et al. Super-critical and critical traveling waves in a three-component delayed disease system with mixed diffusion[J].Journal of Computational and Applied Mathematics,2020,367: 112451.

[15]WU J H, ZOU X F. Traveling wave front solutions in reaction-diffusion systems with delay[J].Journal of Dynamics and Differential Equations,2001,13: 651-687.

[16]CHEN X F, GUO J S. Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics[J].Mathematische Annalen,2003,326: 123-146.

[17]FU S C. Traveling waves for a diffusive SIR model with delay[J].Journal of Mathematical Analysis and Applications,2016,435(1): 20-37.

[18]WEI J D, ZHEN Z L, ZHOU J B, et al. Traveling waves for a discrete diffusion epidemic model with delay[J].Taiwanese Journal of Mathematics,2021,25(4): 831-866.

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