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一类具有非线性发生率与时滞的非局部扩散SIR模型的临界波的存在性

张秋 陈广生

张秋, 陈广生. 一类具有非线性发生率与时滞的非局部扩散SIR模型的临界波的存在性[J]. 应用数学和力学, 2019, 40(7): 713-727. doi: 10.21656/1000-0887.390208
引用本文: 张秋, 陈广生. 一类具有非线性发生率与时滞的非局部扩散SIR模型的临界波的存在性[J]. 应用数学和力学, 2019, 40(7): 713-727. doi: 10.21656/1000-0887.390208
ZHANG Qiu, CHEN Guangsheng. Existence of Critical Traveling Waves for Nonlocal Dispersal SIR Models With Delay and Nonlinear Incidence[J]. Applied Mathematics and Mechanics, 2019, 40(7): 713-727. doi: 10.21656/1000-0887.390208
Citation: ZHANG Qiu, CHEN Guangsheng. Existence of Critical Traveling Waves for Nonlocal Dispersal SIR Models With Delay and Nonlinear Incidence[J]. Applied Mathematics and Mechanics, 2019, 40(7): 713-727. doi: 10.21656/1000-0887.390208

一类具有非线性发生率与时滞的非局部扩散SIR模型的临界波的存在性

doi: 10.21656/1000-0887.390208
基金项目: 国家自然科学基金(面上项目)(11671315)
详细信息
    作者简介:

    张秋(1989—),女, 硕士生(通讯作者. E-mail: 1204142234@qq.com);陈广生(1979—), 男, 博士生(E-mail: cgswavelets@126.com).

  • 中图分类号: O175.14

Existence of Critical Traveling Waves for Nonlocal Dispersal SIR Models With Delay and Nonlinear Incidence

Funds: The National Natural Science Foundation of China(General Program)(11671315)
  • 摘要: 研究了一类具有时滞的非局部扩散SIR传染病模型的行波解。首先, 利用反证法证明了I是有界的, 并根据I的有界性研究了波速c>c*时行波解(波速大于最小波速的行波)的存在性。其次,利用c>c*的行波的存在性结果证明了临界波(波速等于最小波速的行波)的存在性。最后, 讨论了R0对临界波存在性的影响.
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出版历程
  • 收稿日期:  2018-07-26
  • 修回日期:  2018-11-09
  • 刊出日期:  2019-07-01

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