A fish harvesting model with Allee effect and Holling type II functional response

Abstract

Fish harvesting is one of the most profitable investments as it does not require financial costs other than fishing equipment. Therefore, population harvesting models have become attractive to many researchers in the field of mathematical bio-economics. With so many models of fish harvesting, few of them discuss the use of Holling type II functional response to model the interaction between fish populations, harvest effort, and the conditions that are necessary to sustain fish harvesting in the long term. In this paper, we first present a differential equations model describing the dynamics of the fishes population under the presence of harvesting activity. We assume that, in the absence of harvesting activities, the growth dynamics of the fishes population is governed by a logistic growth with Allee effect. The harvesting term is represented by Holling type II functional response. The existence conditions for positive equilibrium point are derived, and the stability of the model equilibrium points are analyzed. An explicit fitted numerical method that is much faster than the Matlab’s ODE solvers is developed to solve the model. Finally, numerical simulations are used to confirm the theoretical results.