2021/2023 UNC Greensboro PDE Conference.
Electron. J. Diff. Eqns., Conference 26 (2022), pp. 219-242.

Title: Traveling wave solutions for an epidemic model

Author: Zhenbu Zhang (Jackson State Univ., Jackson, MS, USA)
 
Abstract: 
In this article, we  consider a one-dimensional reaction-diffusion 
epidemic model, which is neither cooperative nor competitive. 
We study the possible impact of the spatial movement by investigating 
the existence of traveling wave solutions.
 We construct a pair of upper-lower solutions and then use Shauder's 
fixed point theorem to prove the existence of nonnegative nontrivial 
bounded semi-traveling wave solution. 
This is done by introducing a critical wave speed depending on the 
diffusion coefficients and other parameters in the model 
such that, for the wave speed that is greater than the critical wave speed, 
the model has such a solution. 
We also derive a condition under which 
the model has no nonnegative nontrivial bounded semi-traveling wave solution

Published May 13, 2025.
Math Subject Classifications: 35C07, 35K57, 35Q92.
Key Words: Reaction-diffusion; traveling waves; equilibrium; wave speed; basic reproduction number; upper-lower solutions.