Implementation of the Runge- Kutta Method and SIR Model to Understand Covid-19 Spread in Padang City

The spread of the COVID-19 pandemic became a global concern after the outbreak was first reported in Wuhan, China in December 2019. This pandemic had a serious impact on public health, the economy, and social life. The Indonesian government was also not immune with COVID-19 cases fluctuating significantly. West Sumatra Province, especially Padang City, experienced significant fluctuations in case numbers during the peak of the pandemic. Although the World Health Organization has recently rescinded its highest-level alert status for the coronavirus pandemic, understanding the dynamics of disease spread remains crucial for future preparedness and response to potential outbreaks. One approach used is mathematical modeling, including the SIR (Susceptible-Infectious-Removed) model. This model has proven effective in understanding the dynamics of infectious disease spread. This research uses the SIR model with the Runge-Kutta Order 4 numerical method to model the spread of COVID-19 in Padang City. We employed the L-BFGS-B optimization algorithm to estimate the model parameters. The research results show that a transmission rate (β) of 0.906 and a recovery rate (γ) of 0.803 provide the best fit to the observed data, yielding a Root Mean Square Error (RMSE) of 74.251. These boundary values were acquired by limiting the distinction between the model expectations and the genuine Coronavirus case information for Padang City. Therefore, this research can make an important contribution to understanding and managing future disease outbreaks at the local level, as well as offering a useful tool for policy makers to take appropriate steps in epidemic preparedness and response.