Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 49, pp. 1-21.

Title: Stability of bistable traveling wavefronts for a nonlocal dispersal epidemic system
       
Authors: Yu-Cai Hao    (Northwest Normal Univ., Lanzhou, Gansu, China)
         Guo-Bao Zhang (Northwest Normal Univ., Lanzhou, Gansu, China)

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.