Uniqueness and exponential stability of traveling wave fronts for a multi-type SIS nonlocal epidemic model

This paper is concerned with the traveling wave fronts of a multi-type SIS nonlocal epidemic model. From Weng and Zhao (2006), we know that there exists a critical wave speed c∗>0 such that a traveling wave front exists if and only if its wave speed is above c∗. In this paper, we first prove the uniqueness of certain traveling wave fronts with non-critical wave speed. Then, we show that all non-critical traveling wave fronts are asymptotically exponentially stable. The exponential convergent rate is also obtained.