An SIS epidemic model with diffusion  

作　　者：XU Zhi-ting CHEN Dan-xia 

机构地区：[1]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2017年第2期127-146,共20页高校应用数学学报（英文版）（B辑）

基　　金：Partially supported by the NSF of Guangdong Province(2016A030313426);the HLUCF of South China Normal University(2016YN30)

摘　　要：The aim of this paper is to study the diffusion. We first study the well-posedness of the dynamics of an SIS epidemic model with model. And then, by using linearization method and constructing suitable Lyapunov function, we establish the local and global stability of the disease-free equilibrium and the endemic equilibrium, respectively. Furthermore, in view of Schauder fixed point theorem, we show that the model admits traveling wave solutions con- necting the disease-free equilibrium and the endemic equilibrium when R0 〉 1 and c 〉 c^＊. And also, by virtue of the two-sided Laplace transform, we prove that the model has no traveling wave solution connecting the two equilibria when R0 〉 1 and c ∈（0, c^＊）.The aim of this paper is to study the diffusion. We first study the well-posedness of the dynamics of an SIS epidemic model with model. And then, by using linearization method and constructing suitable Lyapunov function, we establish the local and global stability of the disease-free equilibrium and the endemic equilibrium, respectively. Furthermore, in view of Schauder fixed point theorem, we show that the model admits traveling wave solutions con- necting the disease-free equilibrium and the endemic equilibrium when R0 〉 1 and c 〉 c^＊. And also, by virtue of the two-sided Laplace transform, we prove that the model has no traveling wave solution connecting the two equilibria when R0 〉 1 and c ∈（0, c^＊）.

关 键 词：SIS epidemic model traveling wave solution local stability global stability diffusive. 

分 类 号：O175[理学—数学]