A mathematical model for assessing the impact of dual-level toxicity on aquatic biospecies and its optimal control analysis

K. O. Achema; D. Okuonghae; C. J. Alhassan; K. O. Achema; D. Okuonghae; C. J. Alhassan

doi:10.3934/mmc.2022012

Mathematical Modelling and Control

2022, Volume 2, Issue 3: 100-121. doi: 10.3934/mmc.2022012

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A mathematical model for assessing the impact of dual-level toxicity on aquatic biospecies and its optimal control analysis

1.
Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
2.
Department of Mathematics, University of Benin, Benin City, Nigeria
3.
Department of Mathematics and Computer Science, Edo State University, Uzairue, Edo State, Nigeria

Received: 28 January 2022 Revised: 26 May 2022 Accepted: 19 July 2022 Published: 27 September 2022

Ecological models have become paramount for assessing the pesticides effect on the function and structure of aquatic ecosystems. The most paramount concerns are assessments of pesticides/toxicants that have the potential to change from one form to another when they are released into the aquatic ecosystem. Optimal control model is formulated from the nonlinear mathematical model for assessing dual-level toxicity of pesticides effect on aquatic species with the goal to minimizing the pesticides concentration in the aquatic species environment and maximizing the aquatic species population. Two control functions were introduced to represent a policy of not allowing pesticides concentration into the aquatic species environment and the removal of those pesticides that are already in the aquatic environment. The resulting optimal controls are characterized in terms of the optimality system and it was solved quantitatively for different scenarios using both forward and backward sweep iterative method with Runge-Kutta fourth order scheme. The result of the system showed different levels of the aquatic species population stability due to the different levels of the pesticides influx. It was also observed that the degradation of pesticides concentration causes pesticides concentration to vary significantly between the water body and the sediment region with significant level effect on the aquatic species.
- optimal control,
- biodegradable pesticides,
- water,
- sediments,
- aquatic biospecies
Citation: K. O. Achema, D. Okuonghae, C. J. Alhassan. A mathematical model for assessing the impact of dual-level toxicity on aquatic biospecies and its optimal control analysis[J]. Mathematical Modelling and Control, 2022, 2(3): 100-121. doi: 10.3934/mmc.2022012

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Abstract

Ecological models have become paramount for assessing the pesticides effect on the function and structure of aquatic ecosystems. The most paramount concerns are assessments of pesticides/toxicants that have the potential to change from one form to another when they are released into the aquatic ecosystem. Optimal control model is formulated from the nonlinear mathematical model for assessing dual-level toxicity of pesticides effect on aquatic species with the goal to minimizing the pesticides concentration in the aquatic species environment and maximizing the aquatic species population. Two control functions were introduced to represent a policy of not allowing pesticides concentration into the aquatic species environment and the removal of those pesticides that are already in the aquatic environment. The resulting optimal controls are characterized in terms of the optimality system and it was solved quantitatively for different scenarios using both forward and backward sweep iterative method with Runge-Kutta fourth order scheme. The result of the system showed different levels of the aquatic species population stability due to the different levels of the pesticides influx. It was also observed that the degradation of pesticides concentration causes pesticides concentration to vary significantly between the water body and the sediment region with significant level effect on the aquatic species.

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