Global stability of travelling waves for a class of monostable epidemic models

We study the stability of travelling wave solutions for a monostable reaction-diffusion system which describes the spatial spread of a class of bacterial and viral in man-environment diseases. Mathematically we prove the global stability of traveling wave solutions with any admissible wave speed (including the critical wave speed) for the system, and compute numerically the critical wave speed and solutions of the cauchy problem with given initial functions close to the travelling waves at the wave tail for some reaction functions to show the global stability of traveling wave solutions with noncritical wave speed and critical wave speed, respectively. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

The study investigates the stability of travelling wave solutions for a monostable reaction-diffusion system describing the spatial spread of bacterial and viral diseases in the human-environment. Global stability of travelling wave solutions with any admissible wave speed, including the critical wave speed, is proven mathematically. Numerical computation of the critical wave speed and solutions of the Cauchy problem further demonstrate the global stability of travelling wave solutions with noncritical wave speed and critical wave speed.