Modelling and optimal control of toxicants on fish population with harvesting

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 study, a model for controlling toxicants is formulated and analysed. Boundedness, positivity and analysis of the model are examined where four steady states were 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 graphs show that when there is no control applied, population decreases due to effect of toxic and when control is applied the result reveals that the amount of toxic is reduced and hence there is an increase in fish population for both prey and predator population. It is recommended that the government has to introduce laws and policies which ensure that the industries treat waste before they are discharged into water bodies and to develop a system for waste recycling.