# Travelling waves for a bistable reaction-diffusion equation with delay

## TL;DR

This paper establishes the existence of travelling wave solutions in a delayed bistable reaction-diffusion model related to immune response, using Leray-Schauder methods without assuming quasi-monotonicity.

## Contribution

It proves the existence of travelling waves in a delayed reaction-diffusion equation without requiring quasi-monotonicity, extending previous results.

## Key findings

- Existence of travelling wave solutions proven
- Application of Leray-Schauder method to delayed equations
- No quasi-monotonicity assumption needed

## Abstract

The paper is devoted to a reaction-diffusion equation with delay arising in modelling the immune response. We prove the existence of travelling waves in the bistable case using the Leray-Schauder method. In difference with the previous works, we do not assume here quasi-monotonicity of the delayed reaction term.