Stability property of the predator-free equilibrium of a predator-prey-scavenger model with fear effect and quadratic harvesting

Abstract

This article investigates the stability property of predator-free equilibrium of a predator-prey-scavenger model with fear effect and quadratic harvesting. The model was proposed by Mohammed Abdellatif Ahmed and Dahlia Khaled Bahlool (The influence of fear on the dynamics of a prey-predator-scavenger model with quadratic harvesting, Commun. Math. Biol. Neurosci., 2022, 2022: 62). By applying the standard comparison theorem and fluctuation lemma, we show that the conditions which ensure the locally asymptotically stable of predator-free equilibrium are enough to ensure global attractivity. Our result complements and supplements one of the main results of Mohammed Abdellatif Ahmed and Dahlia Khaled Bahlool.