Comparative Analysis of Exponential, Logistic and Gompertz Models for Forecasting Afghanistan's Population up to 2050

Abstract

Good forecasts of population are vital to underpin economic planning, the formulation of public policy and sustainable development. Although many populations growth models have been utilized in demographic studies, limited research has systematically compared their predictive performance for Afghanistan using recent population data. The objective of this study is to forecast the population of Afghanistan up to 2050 by evaluating and comparing the performance of the Exponential, Logistic and Gompertz growth models. United Nations Department of Economic and Social Affairs (UN DESA), Population Division, World Population Prospects 2024 (Online Edition), annual population data 1990–2023. The data set was divided into a training set (1990–2013) and a testing set (2014–2023). The model parameters were estimated using the Nonlinear Least Squares (NLS) method. The model performance was evaluated using the Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and the coefficient of determination (). The results show that the Gompertz model gives the highest predictive accuracy in the testing dataset, outperforming both the Logistic and Exponential models for all evaluation metrics. The best model predicts Afghanistan’s population will be about 83.24 million in 2050. Such findings could provide valuable evidence for demographic forecasting and can support policymakers in long-term planning, resource allocation, infrastructure development and sustainable development strategies in Afghanistan.