Impact of Fear, Allee Effects, and Harvesting on a Predator-Prey Delay Model with a Modified Beddington–DeAngelis Functional Response

Abstract

This paper studies the dynamics of a delayed predator-prey model with a modified Beddington-DeAngelis response function influenced by fear factors, Allee effects, and harvesting on the predator population. This paper analyzes the influence of parameters, namely fear factors ($\omega$), Allee effects ($m$), and delay time ($\tau$), on the stability of the model’s equilibrium point. First, an analysis of the existence of the model’s equilibrium point is carried out, then an analysis of the stability and the influence of changes in the model’s parameter values and delay time that can affect the stability of the model’s equilibrium point is carried out. The analysis indicates that the larger the parameters $\omega$, $m$, and $\tau$, the more unstable the coexistence equilibrium point tends to be. Several numerical simulation results are used to validate the analytical results obtained.