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 functi...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^*).展开更多
基金Partially supported by the NSF of Guangdong Province(2016A030313426)the HLUCF of South China Normal University(2016YN30)
文摘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^*).