Electron. J. Differential Equations, Vol. 2022 (2022), No. 49, pp. 1-21.

Stability of bistable traveling wavefronts for a nonlocal dispersal epidemic system

Yu-Cai Hao, Guo-Bao Zhang

Abstract:
This article concerns the stability of traveling wavefronts for a nonlocal dispersal epidemic system. Under a bistable assumption, we first construct a pair of upper-lower solutions and employ the comparison principle to prove that the traveling wavefronts are Lyapunov stable. Then, applying the squeezing technique combining with appropriate upper-lower solutions, we show that the traveling wavefronts are globally exponentially stable. As a corollary, the uniqueness of traveling wavefronts is obtained.

Submitted October 27, 2021. Published July 12, 2022.
Math Subject Classifications: 35K57, 35B35, 92D30.
Key Words: Epidemic system; nonlocal dispersal; bistable traveling waves; stability.
DOI: https://doi.org/10.58997/ejde.2022.49

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Yu-Cai Hao
College of Mathematics and Statistics
Northwest Normal University
Lanzhou, Gansu 730070, China
email: 626526834@qq.com
Guo-Bao Zhang
College of Mathematics and Statistics
Northwest Normal University
Lanzhou, Gansu 730070, China
email: zhanggb2011@nwnu.edu.cn

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