Mathematical models are essential tools for understanding the transmission dynamics of infectious diseases and for evaluating effective control strategies. This paper investigates a classical SIR (Susceptible–Infected–Recovered) epidemiological model formulated as a system of ordinary differential equations for a closed population. The model behavior is analyzed using analytical methods and numerical simulations to examine the influence of key parameters, including transmission and recovery rates, on disease progression. The results illustrate the conditions under which an epidemic emerges, reaches a peak, and eventually declines. The study highlights the significance of parameter variation in controlling disease spread and demonstrates the applicability of differential equation–based models in supporting public health planning and decision-making.
Epidemiological modeling, SIR model, infectious diseases, differential equations, epidemic dynamics, numerical simulation, disease transmission, mathematical modeling.
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