This research investigates continuous-time population dynamics using mathematical modelling techniques based on ordinary differential equations (ODEs). It focuses on both single-species and multi-species models to understand how populations evolve under various biological and environmental factors. Classical models, including exponential and logistic growth, are analysed to describe population behaviour under ideal and resource-limited conditions. The study is then extended by introducing the Birth Immigration Death Emigration (BIDE) model, which incorporates key processes affecting population change. Furthermore, the research examines equilibrium (steady state) solutions and structural stability using linear stability analysis. Graphical tools such as phase-line diagrams and time-series representations are used to illustrate system behavior. In addition, interacting populations are modeled using systems of differential equations to study ecological interactions such as competition, predator–prey dynamics, and mutualism. The results show how mathematical models can predict long-term population behavior, including growth, stabilization, oscillation, or extinction. Overall, this study highlights the importance of continuous-time models as powerful tools in mathematical biology, with applications in ecology, conservation, and resource management. Keywords: Continuous-Time Models; Population Dynamics; BIDE Model; Logistic Growth; Stability Analysis.
