Dynamical analysis and optimal harvesting policy of a prey-predator model with Holling type-III functional response

Abstract

In this study, we propose and analyze a two-dimensional prey-predator model with the harvesting of both prey and predator. The species are harvested according to the catch-per-unit effort (CPUE) hypothesis. It is assumed that the predator is partially dependent upon the prey population and followed by Holling type-III functional response. Steady states of the system are obtained, and local and global stability analysis is performed to examine the long-term behavior of the system. We also examine the effect of harvesting on the dynamics of the system. It is noticed that for higher values of harvesting efforts, the prey population becomes extinct via a transcritical bifurcation. We derive an optimal harvesting policy and obtain the optimal steady state solution and optimal harvesting efforts using Pontryagin’s Maximum Principle. Lastly, some numerical illustrations are presented in support of our theoretical findings. For a chosen set of parameters, we obtain the threshold value of some parameters beyond which the harvesting of prey biomass must be stopped for the sustainable growth of the species.