Mathematical Modeling of Population Growth Using Differential Equations

Population growth is a central topic in mathematical biology and ecological modeling. This paper analyzes population dynamics using exponential, logistic, and extended nonlinear models. The study formulates first-order differential equations to describe how populations evolve over time under different environmental constraints. Analytical solutions are derived for classical models, while advanced extensions such as harvesting effects, Allee thresholds, time-dependent growth rates, delayed feedback systems, and predator–prey interactions are also introduced. Results show that exponential models describe ideal conditions, while logistic and nonlinear models provide realistic and stable long-term population behavior.