Department of Mathematics and Statistical Sciences
Jackson State University
Jackson, MS 39217, USA
email: zhenbu.zhang@jsums.edu
Zhenbu Zhang
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
DOI: https://doi.org/10.58997/ejde.conf.26.z1
Show me the PDF file (389 K), TEX file for this article.
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Zhenbu Zhang Department of Mathematics and Statistical Sciences Jackson State University Jackson, MS 39217, USA email: zhenbu.zhang@jsums.edu |
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