Uniqueness and exponential stability of traveling wave fronts for a multi-type SIS nonlocal epidemic model. (August 2017)

• Record Type: Journal Article
• Authors: Wu, Shi-Liang; Chen, Guangsheng
• Is Part Of: Nonlinear analysis. Volume 36(2017)
• Page Start: 267
• Page End: 277
• Publication Date: 2017-08
• Subjects: SIS nonlocal epidemic model -- Traveling wave front -- Uniqueness -- Stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.02.001
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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.