An SIS epidemic model with diffusion

作者：Xu Zhi-ting^*; Chen Dan-xia

来源：Applied Mathematics. Series B, A Journal of Chinese Universities, 2017, 32(2): 127-146.

DOI：10.1007/s11766-017-3460-1

• SIS epidemic model
• traveling wave solution
• local stability
• global stability
• diffusive

The aim of this paper is to study the dynamics of an SIS epidemic model with diffusion. We first study the well-posedness of the 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 connecting the disease-free equilibrium and the endemic equilibrium when R (0) > 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 R (0) > 1 and c a [0, c*).

• 出版日期2017-6