Modeling and Optimization of Interaction between Small Coastal Pelagic Fish, their Biological Predators and Fishermen

Abstract

Small coastal pelagic fish are one of the fish families most affected by sea fishing. This man-made phenomenon leads to an imbalance in the marine and coastal ecosystem and is one of the main causes of migration north and offshore of the ranges. We used the ordinary differential equations to model the interactions existing between small pelagic resources and fishermen. Modelling follows the same of the Lotka-Volterra equations with a difference in the number of variables. This study confirmed the instability of the marine ecosystem. The objective is first of all to model a system of three interacting individuals composed of two distinct types of predators and two types of prey, and then optimise this interaction with the aim of conserving biodiversity in the ecosystem under study. Determining the Jacobian matrix made it possible to calculate the reproduction rate basic (R0). The study of the strong connectedness has made it possible to reduce the number of variables without losing the objective of the study. A computer program implemented on the language computer python facilitated the visualisation of the results.