Solving and Plotting Initial Value Problems for SIR Differential Equation Models

This document addresses the solution and graphical representation of SIR differential equation models, which are fundamental for describing disease transmission dynamics. The model classifies populations into three compartments: Susceptible (S), Infected (I), and Recovered (R). The system of differential equations enables predictions about disease spread patterns and supports evidence-based intervention planning. In computational implementations, numerical methods like Runge-Kutta algorithms (e.g., ode45 in MATLAB) are typically employed to solve the coupled nonlinear equations, while visualization libraries (Matplotlib in Python or plot in MATLAB) generate time-series plots of compartmental transitions. The SIR model plays a critical role in epidemiological research, where numerical solving and plotting facilitate deeper understanding of model behavior and predictive capabilities—particularly through parameter sensitivity analysis and reproductive number (R0) calculations.