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

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.