摘要
研究了一类具有时滞和空间扩散的SIR传染病模型,通过分析相应的特征方程,讨论了系统每个平衡态的局部稳定性,通过运用交叉迭代方法和Schauder不动点定理,把行波解的存在性转化为一对上下解的存在性,通过构造一对上下解,得到了连接无病平衡态和地方病平衡态的行波解的存在性.
A delayed SIR epidemic model with spatial diffusion is investigated in this paper. By analyzing the corresponding characteristic equations, the local stability of each of uniform steady states to this system is discussed. By using a cross iteration scheme and Schauder＇s fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.
作者
李海萍
LI Hai-ping(College of Sciences,Hebei University of Science and Technology,Shijiazhuang 050018,China)
出处
《数学的实践与认识》
北大核心
2018年第12期292-295,共4页
Mathematics in Practice and Theory
基金
河北省软科学研究计划项目(154576318)
关键词
行波解
SIR传染病模型
时滞
空间扩散
traveling wave solutions
SIR epidemic model
delay
spatial diffusion
