留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

张笑嫣. 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[J]. 应用数学和力学, 2021, 42(12): 1317-1326. doi: 10.21656/1000-0887.420111
引用本文: 张笑嫣. 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[J]. 应用数学和力学, 2021, 42(12): 1317-1326. doi: 10.21656/1000-0887.420111
ZHANG Xiaoyan. Existence of Critical Traveling Wave Solutions for a Class of Discrete Diffusion SIR Models With Nonlinear Incidence and Time Delay[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1317-1326. doi: 10.21656/1000-0887.420111
Citation: ZHANG Xiaoyan. Existence of Critical Traveling Wave Solutions for a Class of Discrete Diffusion SIR Models With Nonlinear Incidence and Time Delay[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1317-1326. 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
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

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

  • 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.
  • 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.
  • 加载中
计量
  • 文章访问数:  195
  • HTML全文浏览量:  35
  • PDF下载量:  49
  • 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

目录

    /

    返回文章
    返回