Effects of harvesting and planktivorous fish on bioeconomic phytoplankton-zooplankton models with ratio-dependent response functions and time delays

Abstract

This work presents a prey-predator model for plankton interactions in aquatic environments and the influence of planktivorous fish predation. Considering that some phytoplankton and zooplankton can be harvested due to their economic value, the time lag required for zooplankton gestation (representing the time delay) is included. The current study's main objective is to analyze planktivorous fish's influence on harvesting activity in both populations and the corresponding discrete delay (delay in zooplankton gestation) in the model. The stability characteristics of models with and without gestation delay are investigated, and the gestation delays threshold value is determined. The periodic solution's stability and the Hopf bifurcations' direction are determined by employing the center manifold theory. We use Lyapunov's method to investigate the global stability of the model without time delay. Bioeconomic equilibrium is obtained in three cases, each with certain conditions. In addition, the optimal harvesting strategy from the model is obtained by using the Pontryagin Maximum Principle and considering harvesting effort as a control variable. Finally, numerical simulations are performed to illustrate our analytical findings, and the ecological implications of our analytical findings are also discussed.