Dynamical Analysis of Two-Preys and One Predator Interaction Model with An Allee Effect on Predator

Abstract

Mathematical modeling in biology is quite interesting in the field of real-world problems. This research paper focused on the interaction between two prey and one predator species. Here, our interaction is based upon the competition between two prey and one predator including an additive Allee effect in the predator population along with a Holling type II functional response. Further, this intuition allowed us to prove the positive invariance and boundedness of the model. This analysis shows that there are six equilibrium points including the coexistence of all three populations. Stability analyses are also derived and proved both locally and globally. Also in this paper, we discussed the optimal control approach to reduce the population affected by an Allee effect by the predator population. Numerical simulations are carried out to support our theoretical results.