Population Growth Prediction Using Logistic-Based Grey Forecasting Model

Abstract

Population growth prediction is a critical task for effective policy-making and planning, impacting economic development, social stability, and resource utilization. Traditional models like the Malthusian and logistic growth models have been foundational in understanding population dynamics. However, these models have limitations, particularly in accounting for resource constraints and technological advancements. To address these limitations, this study develops and validates a logistic-based grey prediction model for population growth. The logistic-based grey prediction model integrates the logistic growth model's characteristics with grey system theory, which is designed for systems with incomplete or uncertain information. This integration enhances the model's robustness and accuracy in population forecasting. The model leverages the least squares method for parameter estimation and employs a weakening buffer operator to refine predictions. Empirical analyses using population data from various periods demonstrate the model's effectiveness and improved accuracy. The study also compares the logistic-based grey prediction model with other numerical methods, including the Taylor Series Method, Central Difference Methods, and the Leslie Model. The results indicate that the logistic-based grey prediction model provides reliable forecasts, making it a valuable tool for policymakers and researchers. The findings suggest that the logistic-based grey prediction model can better accommodate fluctuations in population data and offer more accurate long-term predictions. This contributes to more informed decision-making in demographic and economic planning, highlighting the model's practical application in real-world scenarios.