Revista de Matemática Aplicada e Computacional

Modelling and Optimal Control of Toxicants on Fish Population with Harvesting

Abstract

Zachariah Noboth, Estomih S. Massawe* Daniel O. Makinde, Lathika .P

Toxic in water bodies is a worldwide problem. It kills fish and other aquatic animals in water. Human beings are affected by this indirectly through eating affected fish.

In this paper, a model for controlling toxicants in water is formulated and analysed. Boundedness, positivity and analysis of the model are examined where four steady

states are determined by using Eigen-value analysis and found to be locally stable under some conditions. The optimal control strategies are established with the help

of Pontryagin’s maximum principle. The simulations for the model with control show that when control is applied the results reveals that the amount of toxic is reduced

and hence there is an increase in fish population for both prey and predator populations. It is recommended that the government has to introduce laws and policies

which ensure that the industries treat waste water before they are discharged into water bodies and to develop a system for waste recycling