Modeling and estimation in aquaculture ponds based on bioenergetic fish growth models

Sharefa Asiri; Salma Al-Tuwairqi; Sara Al-Amoudi; Sharefa Asiri; Salma Al-Tuwairqi; Sara Al-Amoudi

doi:10.3934/math.2026450

AIMS Mathematics

2026, Volume 11, Issue 4: 10963-10985. doi: 10.3934/math.2026450

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Research article

Modeling and estimation in aquaculture ponds based on bioenergetic fish growth models

Department of Mathematics, King Abdulaziz University, Jeddah 1540, Saudi Arabia

Received: 18 February 2026 Revised: 05 April 2026 Accepted: 08 April 2026 Published: 20 April 2026
MSC : 34Dxx, 91-10, 81P50

Aquaculture is a vital component in meeting the increasing demand for food by providing a sustainable alternative to traditional sources that are no longer sufficient to cover future needs. In this paper, we focused on studying the fundamental factors influencing the performance of aquaculture systems, where the accumulation of unionized ammonia (UIA) represents one of the most critical challenges directly affecting fish health, growth, and population density within ponds. In this work, a bioenergetic mathematical model for fish growth was developed to accurately represent the system dynamics through the integration of UIA effects and their relationship with total fish biomass ($ \xi $) and fish population ($ P $). The model was analyzed using qualitative mathematical tools to verify the positivity and boundedness of the state variables, determine equilibrium points, and assess their stability. Moreover, numerical simulations were performed to capture the growth dynamics under different conditions. In addition, the modulating function method was applied to estimate the UIA concentration.
- aquaculture,
- mathematical model,
- bioenergetic growth,
- unionized ammonia,
- stability analysis,
- modulating function method
Citation: Sharefa Asiri, Salma Al-Tuwairqi, Sara Al-Amoudi. Modeling and estimation in aquaculture ponds based on bioenergetic fish growth models[J]. AIMS Mathematics, 2026, 11(4): 10963-10985. doi: 10.3934/math.2026450

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Abstract

Aquaculture is a vital component in meeting the increasing demand for food by providing a sustainable alternative to traditional sources that are no longer sufficient to cover future needs. In this paper, we focused on studying the fundamental factors influencing the performance of aquaculture systems, where the accumulation of unionized ammonia (UIA) represents one of the most critical challenges directly affecting fish health, growth, and population density within ponds. In this work, a bioenergetic mathematical model for fish growth was developed to accurately represent the system dynamics through the integration of UIA effects and their relationship with total fish biomass ($ \xi $) and fish population ($ P $). The model was analyzed using qualitative mathematical tools to verify the positivity and boundedness of the state variables, determine equilibrium points, and assess their stability. Moreover, numerical simulations were performed to capture the growth dynamics under different conditions. In addition, the modulating function method was applied to estimate the UIA concentration.

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