Wave propagation of a discrete SIR epidemic model with a saturated incidence rate  

作　　者：Qiu Zhang Shi-Liang Wu 

机构地区：[1]School of Mathematics and Statistics, Xidian University Xi7an, Shaanxi 710071, P. R. China

出　　处：《International Journal of Biomathematics》2019年第3期109-126,共18页生物数学学报（英文版）

摘　　要：This paper is concerned with the traveling wave solutions for a discrete SIR epidemic model with a saturated incidence rate. We show that the existence and non-existence of the traveling wave solutions are determined by the basic reproduction number R0 of the corresponding ordinary differential system and the minimal wave speed c*. More specifically, we first prove the existence of the traveling wave solutions for R0>1 and c>c* via considering a truncated initial value problem and using the Schauder’s fixed point theorem. The existence of the traveling wave solutions with speed c=c? is then proved by using a limiting argument. The main difficulty is to show that the limit of a decreasing sequence of the traveling wave solutions with super-critical speeds is non-trivial. Finally, the non-existence of the traveling wave solutions for R0>1,0<c<c* and R0≤1,c>0 is proved.

关 键 词：LATTICE dynamic system TRAVELING wave solution EXISTENCE NON-EXISTENCE 

分 类 号：G[文化科学]