On existence of semi-wavefronts for a non-local reaction-diffusion equations with distributed time delay

TL;DR

This paper proves the existence of semi-wavefront solutions in non-local delayed reaction-diffusion equations with monostable nonlinearities, applicable to epidemic and population models with distributed delays, for all speeds above a critical threshold.

Contribution

It establishes the existence of semi-wavefronts for a class of non-local delayed reaction-diffusion equations, extending understanding of wave propagation in such systems.

Findings

Existence of semi-wavefronts for all speeds c ≥ c_*

Determination of the minimal propagation speed c_*

Application to epidemic and population models with distributed delay

Abstract

We establish the existence of semi-wavefronts solutions for a non-local delayed reaction-diffusion equation with monostable nonlinearity. The existence result is proved for all speeds $c\geq c_\star$, where the determination of $c_\star$ is similar to the calculation of the minimal speed of propagation. The results are applied to some non-local reaction-diffusion epidemic and population models with distributed time delay.