具有时空时滞的非局部扩散SIR模型的行波解

邹霞

doi:10.21656/1000-0887.380118

具有时空时滞的非局部扩散SIR模型的行波解

doi: 10.21656/1000-0887.380118

邹霞

西安电子科技大学数学与统计学院, 西安 710071

基金项目: 国家自然科学基金(11671315)

详细信息

作者简介:
邹霞(1989—)，女，硕士(Email: 17792543182@163.com).

中图分类号: O175.14
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- 被引次数: 0
出版历程
- 收稿日期: 2017-05-02
- 修回日期: 2018-04-01
- 刊出日期: 2018-05-15

Traveling Wave Solutions for Nonlocal Dispersal SIR Models With Spatio-Temporal Delays

ZOU Xia

School of Mathematics and Statistics, Xidian University, Xi’an 710071, P.R.China

Funds: The National Natural Science Foundation of China(11671315)

摘要

摘要: 针对种群中的染病个体在疾病潜伏期内具有自由移动和传染疾病的现象, 研究了一个具有时空时滞的非局部扩散SIR模型的行波解问题.利用基本再生数和最小波速判定行波解是否存在.首先, 通过在有界区域上构造一个初始函数的不变锥, 利用Schauder不动点定理证明在该锥上存在不动点, 然后通过取极限的方法得到行波解的存在性.其次, 利用双边Laplace(拉普拉斯)变换法证明了行波解的不存在性.由于行波解的最小传播速度对控制疾病传播具有重要的指导意义, 最后讨论了非局部扩散、时滞等因素对最小波速的影响.
- 非局部扩散 /
- 行波解 /
- SIR模型 /
- Schauder不动点定理
Abstract: In view of the infected individuals with the ability to move freely and spread disease, the traveling wave solutions for nonlocal dispersal SIR models with spatiotemporal delays were investigated. The threshold dynamics was determined by means of the basic reproduction number and the minimal wave speed. Firstly, based on Schauder’s fixed point theorem, the existence of fixed points on the cone was proved through construction of an invariant cone of the initial function on a bounded region. Then, the nonexistence of traveling wave solutions was verified through the twosided Laplace transform. Since the minimum propagation velocity of the traveling wave solution had important practical significance to control the disease transmission, the influences of the nonlocal diffusion term and the delay on the minimum wave velocity of the disease were discussed.
- nonlocal dispersal /
- traveling wave solution /
- SIR model /
- Schauder’s fixed point theorem

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参考文献(20)

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