Population growth in developing economies presents complex challenges, requiring robust models to inform sustainable policy interventions. This literature review examines the classical Stochastic Logistic Growth Models (SLGMs), and proposes a Population Dynamics Extension to it as an advanced framework integrating stochasticity, carrying capacity and population dynamics to better capture real-world demographic fluctuations. Unlike classical logistic models, the Extended SLGM with population dynamics accounts for environmental stressors, economic constraints, and policy-driven population control measures, making it particularly relevant for developing nations grappling with rapid urbanisation and resource scarcity. This review synthesises key studies applying the SLGM and creates scenarios of extensions with births, deaths and migration rates, and resource constraints, highlighting its superiority over deterministic approaches in predicting growth trajectories under uncertainty and over the classical SLGM. Special emphasis is placed on how the model informs policies balancing economic development with demographic stability. Critically, we identify gaps in current research, such as the need for localised parameter calibration and interdisciplinary integration with socio-economic data. By evaluating the extended SLGM with Population Dynamics, its theoretical and empirical contributions will be explored, with its potential as a tool for policymakers seeking evidence-based strategies to manage population growth in developing economies while fostering equitable development.