Analysis of Catfish Production Growth Using Bernoulli’s Differential Equation

Abstract

Catfish (Clarias sp.) is one of the most widely cultivated aquaculture commodities in Indonesia, playing an important role in food security and local economic development. This study applies Bernoulli’s differential equation, which reduces to a logistic model, to evaluate catfish production in Indonesia from 2019 to 2025. Secondary data were obtained from the Ministry of Marine Affairs and Fisheries. Model parameters, including carrying capacity, intrinsic growth rate, and initial production, were estimated to fit the observed data. The results show that the logistic model effectively represents production trends between 2020 and 2024, with an average annual growth rate of approximately 4%. However, the model fails to capture the sharp decline observed in 2025, when actual production dropped by nearly 47%. This discrepancy indicates the presence of external non-linear factors, such as disease, environmental stress, or distribution disruptions, that were not included in the mathematical framework. Therefore, Bernoulli’s differential equation provides a useful baseline for analyzing production growth under normal conditions, while highlighting the need to integrate ecological and managerial considerations for more accurate long-term predictions.