Exponential stability of traveling waves in a nonlocal dispersal epidemic model with delay

Guo-Bao Zhang; Yan Li; Zhaosheng Feng

doi:10.1016/j.cam.2018.05.018

Exponential stability of traveling waves in a nonlocal dispersal epidemic model with delay

Guo-Bao Zhang, Yan Li, Zhaosheng Feng

Źródło

Journal of Computational and Applied Mathematics > 2018 > 344 > C > 47-72

Abstrakt

In this paper, we are concerned with the stability of traveling waves of a nonlocal dispersal epidemic model with delay. In the quasi-monotone case, we prove the exponential stability of traveling wavefronts by the weighted-energy method and the comparison principle, when the initial perturbation around the traveling wavefront decays exponentially as x → − ∞ , but can be arbitrarily large in other locations. In the non-quasi-monotone case, we investigate the exponential stability of traveling waves when the initial perturbation around the traveling wave is properly small in a weighted norm.