The SIR model is one of the simplest mathematical models that can be used to describe outbreaks for many different diseases. The SIR model is formed by 3 simple compartments: Susceptible, Infected, and Recovered individuals. This project focuses on the SIR model and uses it to fit real data of two different disease outbreaks with the Least Squares Method. The first disease is the H1N1 Flu and the outbreak that occurred in 2009 in the United States. Figures were produced with the real data and the estimated SIR model, and conclusions were made based on which regions had better fits. The second disease that was used was the COVID-19 outbreak in 2020 in counties of Oklahoma in the United States. Figures were produced and analyzed to see which ones the SIR model was able to predict most closely. The SIR model will be shown to be a good fit for some locations, while for others, it was not that good of a fit for the two diseases considered in this study.