Plankton interaction model: Effect of prey refuge and harvesting

Abstract

Harmful algal blooms are one of the major threats to aquatic ecosystem. Some phytoplankton species produce toxins during algal bloom and affect other aquatic species as well as human beings. Thus, for the conservation of aquatic habitat, it is much needed to control such phenomenon. In the present study, we propose a mathematical model of toxin-producing phytoplankton and zooplankton species, which follows the Holling Type III functional response. We consider the effect of prey refuge and harvesting on both the species. Boundedness of the proposed model, existence of equilibria, and their stability have been discussed analytically. We also discuss the optimal harvesting policy and existence of bionomic equilibrium. The numerical simulation has also been performed. We identify the control parameters that are responsible for the system dynamics of the model. The parameter prey refuge has a great impact on the dynamics of the model system. Higher value of prey refuge leads to the stable dynamics. Also, the growth rate of phytoplankton acts as a control parameter for the dynamics of the model. The higher value of growth rate of phytoplankton is responsible for oscillatory behavior.

Keywords

• optimal harvesting policy
• stability analysis
• harmful algal blooms
• prey refuge
• bionomic equilibrium
• 92b10
• 37n25
• 92b05