Toxicity impacts on bioeconomic models of phytoplankton and zooplankton interactions

Abstract

The primary aim of this research is to investigate how the presence of toxicity, stemming from phytoplankton, impacts fishing activities, catch levels, and financial returns. It is hypothesized that this toxicity arises when zooplankton accumulates harmful substances while consuming phytoplankton. To achieve this objective, we analyze a model resembling a prey-predator relationship involving phytoplankton. We examine the stable conditions in our model by utilizing eigenvalue analysis and calculate the optimal fishing effort that maximizes profitability for fishermen, employing the concept of generalized Nash equilibrium. Additionally, we explore the most effective harvesting strategy by applying Pontryagin’s maximum principle. In our numerical simulations, we identify the key variables that influence all economic aspects of the model, including fishing effort, catch levels, and benefits. Furthermore, we compare our results with findings from previous research.