带有扩散项和接种的传染病模型的行波解  

Existence of Traveling Waves in a Spatial Infectious Disease Model with Vaccination

作　　者：郭庭光 徐志庭[1] Guo Tingguang;Xu Zhiting(School of Mathematical Sciences, South China Normal University, Guangzhou 510631)

机构地区：[1]华南师范大学数学科学学院,广州510631

出　　处：《数学物理学报（A辑）》2017年第6期1129-1147,共19页Acta Mathematica Scientia

基　　金：广东省自然科学基金(2016A030313426);华南师范大学高水平大学建设经费(2016YN30)~~

摘　　要：该文研究带有扩散项和接种的传染病模型的行波解存在性.首先建立一个带扩散项和接种的具有空间结构的传染病模型,并给出其解适定性.其次,构造一对向量型上、下解,应用Schauder不动点原理和Lyapunov函数方法得到此模型存在连接无病平衡点和有病平衡点的非平凡正行波解.利用稳定流形定理,得到行波指数衰减估计,进而,通过拉普拉斯变换,确定该模型行波解的不存在性.该文的研究技巧对建立高维非合作反应扩散系统行波解存在性提供了有效方法.The current paper is devoted to investigate the existence of traveling waves in a spatial infectious disease model with vaccination. First, we propose a spatial infectious disease model with vaccination, and then study the well-posedness of it. Second, based on constructing a pair of the vector-value upper and lower solutions and the applications of Schauder＇s fixed point theorem, we show that the model admits nontrivial and positive traveling waves connect- ing the disease free equilibrium and the endemic equilibrium. Third, by Laplace transforms, we establish the non-existence of traveling waves for the model, in which the prior estimate of the exponential decay of the traveling wave solutions is obtained by the Stable Manifold Theorem. The approach in this paper provides an effective method to deal with more general high dimensional non-cooperative reaction-diffusion systems.

关 键 词：行波解 传染病模型 Schauder不动点原理 向量型上 下解 拉普拉斯变换 

分 类 号：O175.14[理学—数学]