The role of cleaner fish in a predator-prey model: dynamics and optimal harvesting

Abstract

This study focuses on a predator-prey model that includes a Cleaner Fish. It highlights the crucial role of the Cleaner Fish in the system dynamics, as well as the effect of fishing on the three species. The analysis begins by studying the positivity and boundedness of the solutions to ensure that the populations remain present and limited. The stability of the system is examined around the interior equilibrium point, which represents a state where the populations of prey, predators, and Cleaner Fish maintain balance. The optimal harvesting policy is also investigated, aiming to find the fishing strategy that maximizes the dynamic profit of the species while preserving their sustainability. Finally, numerical simulations using Matlab software are conducted to illustrate the theoretical results obtained.