Optimal Harvesting on a Modified Leslie–Gower Predator–Prey Model Under Fear and Allee Effects on Prey

• Published in: Differential equations and dynamical systems Vol. 32; no. 4; pp. 1067 - 1096
• Main Authors: Halder, Susmita, Bhattacharyya, Joydeb, Pal, Samares
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.10.2024; Springer Nature B.V
• Subjects: Bifurcations; Computer Science; Engineering; Fisheries; Mathematics; Mathematics and Statistics; Original Research; Pontryagin principle; Predator-prey simulation; Predators; Steady state; Optimal harvesting; 92B05; 92D25; Fear effect; Maximum sustainable yield; 92D40; Bionomic equilibrium
• ISSN: 0971-3514; 0974-6870
• DOI: 10.1007/s12591-022-00612-z

In this article, we have analyzed the effect of prey apprehension on a modified Leslie–Gower predator–prey fishery model with Allee effect on the prey population. We investigate the predator–prey dynamics for linear, Holling type II, and Holling type III functional responses of the predator and observed that the systems undergo a sudden change in dynamics from the coexistence steady state to the prey-free steady-state when the level of prey apprehension and the amount of harvesting effort surpass some threshold value. At a low intrinsic growth rate of the predator, the system with type II functional response exhibits a transcritical bifurcation when the harvesting effort crosses the threshold value. We study the dynamic optimization of the harvesting policy by employing Pontryagin’s maximum principle under the three different functional responses of the predator and obtain the harvesting yields corresponding to the dynamic reference point OSY. We also examine the existence of the bionomic equilibrium corresponding to the open access (OA) scenario and compare the combined harvesting yield with the yields obtained from the static reference point MSY and the dynamic reference point OSY. We observe that OSY provides the maximum economic benefit to the fishery compared to MSY and OA.