A mathematical model to analyze effect of harvesting on predator-prey interaction with Beddington-Deangelis functional response

In this paper, the stability analysis of the interaction between two populations of a predator-prey model is discussed. The model under study is a modified Lotka-Volterra predator-prey model where the biliary function used to express the interaction between the two populations is replaced by a modified Beddington-DeAngelis functional response. Moreover, the growth in the prey population is updated into a logistic growth. Stability conditions of several equilibrium points have been discussed. This paper also discusses the effect of harvesters on the stability of the equilibrium point. The study is divided into three parts. First, the growth of the prey population is discussed without its interaction with the predator population. Second, the effect of the coexistence of the predator and prey populations on the growth of the latter is discussed. Third, the local stability of the model is deduced from the equilibrium point of the model. Finally, analytical results are supported by numerical simulations and results. Mathematics Subject Classification 37M20, 37N25