Model Comparison, Uncertainty Quantification and Scenario-Based Projections of Nigeria Population Dynamics Using Classical and Fractional Growth Models

Abstract

Precise population projections are indispensable for the effective formulation of sustainable development strategies, judicious resource allocation, and robust infrastructure development within burgeoning economies. Nigeria, as the most populous nation on the African continent, continues to exhibit substantial demographic expansion, consequently imposing escalating demands upon its healthcare, educational, housing, employment, and food systems. This investigation delves into Nigeria's population dynamics through the application of four distinct growth models: the Exponential, Logistic, Fractional Malthus, and Fractional Logistic models. Annual population data spanning the period 1991–2020 were meticulously calibrated employing a weighted parameter estimation methodology, wherein high weight was accorded to data derived from official census years. Model efficacy was rigorously assessed utilizing a suite of statistical criteria, including Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). Parametric uncertainty was quantified via bootstrap confidence intervals, while comprehensive sensitivity and scenario analyses were executed to explore divergent demographic trajectories. The Fractional Malthus model yielded the optimal fit to Nigeria historical data between 1991-2020, by achieving the lowest RMSE (3.0944) and MAPE (1.9542%) and projected a population of approximately 680million by 2060. The derived fractional order substantiates the presence of memory effects inherent in Nigeria's population growth process. Baseline projections forecast Nigeria's population to attain approximately 680 million by 2060, with plausible confidence bounds ranging from 604 to 727 million. This study introduces a unified fractional demographic modelling framework, which comprehensively integrates memory effects, uncertainty quantification, sensitivity analysis, and policy-oriented scenario planning, thereby constituting a significant extension of extant approaches to long-term population forecasting in developing economies. The findings demonstrate the effectiveness of fractional-order models for long-term demographic forecasting and policy planning. The results demonstrate that fractional-order models, particularly the Fractional Malthus model, provide a more reliable framework for long term population forecasting in Nigeria than classical growth models.