Understanding and predicting the spread of infectious diseases is crucial for public health. This study tries to delve into the world of epidemiological modelling, specifically focusing on the Susceptible-Infectious-Recovered (SIR) model and the estimation of its parameters. This report presents a comprehensive exploration of the application of the SIR epidemiological model to the simulation and analysis of infectious disease spread. The study employs a numerical integration approach, specifically the fourth-order Runge–Kutta method, to simulate the dynamics of the SIR model. Additionally, for optimization of the model the Nelder–Mead optimization algorithm is used. The primary focus is on parameter estimation, intending to fit the model to real-time data and obtain optimal values for the transmission rate (β) and recovery rate (γ). Overall, this chapter contributes to the understanding of epidemiological modelling, numerical simulation techniques, and the practical application of the SIR model in the context of infectious disease dynamics. The results of parameter estimation provide insights into the behaviour of the simulated epidemic and demonstrate the code’s utility in forming public health strategies.