| 一类带全局反应项SIR传染病模型的异宿轨和行波解（英文） |
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| 引用本文： | 王宗毅.一类带全局反应项SIR传染病模型的异宿轨和行波解（英文）[J].应用数学,2019,32(3):559-569. |
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| 作者姓名： | 王宗毅 |
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| 作者单位： | 惠州学院数学与大数据学院 |
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| 基金项目： | Supported by the National Natural Science Foundation of China(11601180);NSF of Guangdong Province(2016A030310100);FDYT in Higher Education of Guangdong(2015KQNCX155);Funds of Huizhou University(HZUXL201522,HZU201806) |
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| 摘 要： | 本文研究一类SIR类型传染病模型的正异宿轨的存在性问题,该类模型通常被视为带全局反应项和非单调型的时滞微分方程组.利用Fraia和黄等发展的Freedholm算子分解及非线性扰动理论,我们研究反应扩散系统的行波解和对应时滞微分方程异宿轨解之间的关联性,并据此证明该系统行波解的存在性和动力学性质.
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| 关 键 词： | 时滞微分方程 反应扩散方程 SIR传染病模型 异宿轨 行波解 |
| 收稿时间： | 2018/7/21 0:00:00 |
Heteroclinic and Traveling Wave Solutions for a SIR Epidemic Model with Nonlocal Response |
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| WANG Zongyi.Heteroclinic and Traveling Wave Solutions for a SIR Epidemic Model with Nonlocal Response[J].Mathematica Applicata,2019,32(3):559-569. |
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| Authors: | WANG Zongyi |
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| Affiliation: | (College of Mathematics and Big Data, Huizhou University, Guangdong 516007, China) |
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| Abstract: | The existence of positive heteroclinic solutions is proved for a class of sir epidemic model with nonlocal interaction and non monotone property. Applying the theory of Fredholm operator decomposition and nonlinear perturbation developed by Faria and HUANG(2006), we study a connection between traveling wave solutions for the reaction-diffusion system and heteroclinic solutions of the associated differential equations. Existence and dynamics of wavefront profile are obtained as a consequence. |
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| Keywords: | Delay ordinary differential equation Reaction-diffusion equation SIR epidemic model Heteroclinic solution Traveling wave solution |
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