Pemodelan Matematika Pertumbuhan Ekonomi Provinsi Banten Menggunakan Model Pertumbuhan Logistik

Abstract

Economic growth is a crucial indicator in measuring the success of regional development. This study aims to construct a mathematical model of economic growth in Banten Province using the Verhulst logistic model approach based on Gross Regional Domestic Product (GRDP) at Constant Market Prices data for the 2015–2025 period. The estimation of the intrinsic growth rate parameter (r) and carrying capacity (K) was performed using the least square method via the Levenberg-Marquardt algorithm implemented in Python. The results show that the intrinsic growth rate (r) is 0.0568 per year (5.68%) and the economic carrying capacity (K) is 1,581,097.43 billion rupiah. Model validation indicates an exceptionally high level of accuracy with a Mean Absolute Percentage Error (MAPE) of 1.8738% and a coefficient of determination ( ) of 0.9656. These findings demonstrate that the logistic model is highly representative in capturing the real growth pattern of Banten Province, despite the anomaly caused by the COVID-19 pandemic downturn in 2020. Projections for the 2026–2035 period indicate a continuous positive growth trend, reaching 768,530.34 billion rupiah by 2035, with a gradual asymptotic deceleration as it approaches its economic carrying capacity.