| 一类带治疗项的非局部扩散SIR传染病模型的行波解 |
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| 引用本文： | 邓栋,李燕.一类带治疗项的非局部扩散SIR传染病模型的行波解[J].数学物理学报(A辑),2020(1):72-102. |
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| 作者姓名： | 邓栋 李燕 |
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| 作者单位： | 重庆工商大学数学与统计学院;西安电子科技大学数学与统计学院 |
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| 基金项目： | 陕西省科技厅资助(2017JQ1024)。 |
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| 摘 要： | 该文主要考虑一类非局部扩散传染病模型的行波解的存在性与不存在性.首先,利用Schauder不动点定理和取极限的方法,得到了行波解的存在性.其次,利用双边拉普拉斯变换和Fubini定理,证明了行波解的不存在性.上述结果表明,最小波速是预测疾病是否传播且以多大速度传播的重要阈值.
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| 关 键 词： | 行波解 非局部扩散 最小波速 双边拉普拉斯变换 |
Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Treatment |
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| Deng Dong,Li Yan.Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Treatment[J].Acta Mathematica Scientia,2020(1):72-102. |
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| Authors: | Deng Dong Li Yan |
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| Institution: | (College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400000;School of Mathematics and Statistics,Xidian University,Xi'an 710126) |
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| Abstract: | This paper is concerned with the existence and nonexistence of traveling wave solutions of a nonlocal dispersal epidemic model with treatment.The existence of traveling wave solutions is established by Schauder's fixed point theorem as well as a limiting argument,while the nonexistence of traveling wave solutions is proved by two-sided Laplace transform and Fubini's theorem.From the results,we conclude that the minimal wave speed is an important threshold to predict how fast the disease invades. |
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| Keywords: | Traveling waves Nonlocal dispersal Minimal wave speed Two-sided Laplace transform |
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