Numerical Analysis of COVID-19 Epidemic Dynamics Using the SIR Model: Implementation with Runge-Kutta Methods

This project presents a comprehensive numerical simulation of COVID-19 transmission dynamics using the classical SIR (Susceptible-Infected-Recovered) model, implemented through the fourth-order Runge-Kutta method. The simulation was based on real epidemic data from Hong Kong and aimed to analyze infection and recovery patterns across a 501-day period.

The project involved:

Mathematical modeling using differential equations.

Numerical solution using a custom Python implementation of the RK4 method.

Data processing, parameter estimation, and result visualization.

Validation using real-world COVID-19 data (R² for infection prediction = 0.847).

Critical discussion of model limitations due to virus variants.

The model demonstrates a practical understanding of epidemiological dynamics, numerical methods, and Python-based simulation