兰州大学机构库 >数学与统计学院
一类没有爆发阈值的非局部时滞SIR模型的行波解
Alternative TitleTraveling Wave Solutions of a Nonlocal Delayed SIR Model without Outbreak Threshold
马骢
Thesis Advisor李万同
2013-05-23
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword爆发阈值 极小波速 捕食者食饵系统
Abstract本文主要研究一类不带阈值的非局部时滞SIR模型的行波解的存性, 不存在性以及解的渐近行为. 由此, 我们得出结论: 在任何固定时刻, 疾病传播的越快, 全空间上被感染的个体就越多, 而恢复或移出率越大全空间上被感染的个体越少. 本文首先研究了具有非局部时滞SIR模型的行波解的存在性. 通过上下解在一个适当的Banach 空间中定义一个有界闭凸子集, 在此有界闭凸子集上构造一个全连续算子, 应用不动点定理得到行波解的存在性. 这些结论表明在对应的常微分系统基本再生数大于1的时候, 疾病可以在全空间传播. 其次通过单调性以及渐近传播理论来研究行波解的渐近行为, 证明任何一个非平凡的有界正行波解渐近行为. 这些结论表明, 这一模型描述的疾病爆发不需要阈值: 在基本再生数大于1的时候, 只要有带病个体, 空间上所有个体都会被感染过. 最后研究具有非局部时滞SIR模型的非平凡行波解的不存在性, 通过比较原理以及双边Laplace 变换讨论了行波波解的不存在性. 这些结论表明: 在基本再生数小于1的时候, 疾病无法传播开来; 同时, 如果基本再生数大于1, 那么疾病的传播速度不会低于一个由感染率等决定的常数. 关键词: 爆发阈值, 极小波速, 捕食者食铒系统.
Other AbstractThis paper is concerned with the existence, nonexistence and asymptotic behavior of traveling wave solutions of a diffusive SIR system with nonlocal delay,which formulate the propagation of disease without outbreak threshold. Moreover,it is proved that at any fixed moment, the faster the disease spreads, the more the individual infects, and the larger the recovery/remove ratio is, the less the individual infects. We firstly study the existence of traveling wave solution for SIR model with nonlocal delays. Through defining a bounded and closed convex set on a suitable Banach space and constructing a completely continuous operator, we can obtain the existence of traveling waves by Schauder’s fixed theorem. We further study the asymptotic behavior of traveling waves by the theory of asymptotic spreading and monotony, proving the asymptotic behavior of any nontrivial bounded positive traveling wave solution. These conclusions show that the disease portrayed by the model can break out without threshold, which means if only the infective exsits, all individuals in the area will be infected when the basic reproduction ratio is larger than 1. Finally, we study the nonexistence of traveling waves by comparison principle and two sided Laplace transform. It is shown that the disease can not spread if the basic reproduction ratio is smaller than 1;and the spread speed will be no less than a constant decided by the infectious rate if the basic reproduction ratio is larger than 1. Key words: Outbreak threshold, minimal wave speed, predator-prey system.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224472
Collection数学与统计学院
Recommended Citation
GB/T 7714
马骢. 一类没有爆发阈值的非局部时滞SIR模型的行波解[D]. 兰州. 兰州大学,2013.
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