A note on a prey-predator model with constant-effort harvesting

TL;DR

This paper examines a prey-predator model incorporating constant-effort harvesting, analyzing its equilibria and stability, and clarifies previous inconsistencies in a model proposed in 2021.

Contribution

It presents a corrected version of a prey-predator model with harvesting, analyzing equilibrium points and their stability, and addresses prior inconsistencies.

Findings

Identification of equilibrium points and their types.

Proof of stability for the meaningful equilibrium.

Clarification of previous model inconsistencies.

Abstract

We study a prey-predator model based on the classical Lotka-Volterra system with Leslie-Gower and Holling IV schemes and a constant-effort harvesting. Our goal is twofold: to present the model proposed by Cheng and Zhang in 2021, pointing out some inconsistencies; to analyse the number and type of equilibrium points of the model. We end by proving the stability of the meaningful equilibrium point, according to the distribution of the eigenvalues.