The SIR (Susceptible-Infected-Recovered) models are used to help predict the spread of diseases. The goals of this paper are: elaborating on the methods of approximating the recovery rate, infection rate, and loss of immunity rate, comparing the SIR models with these approximation methods to real world data, and determining the most accurate combination of the approximation methods for each SIR model. There are several SIR models such as the Kermack-McKendrick, SIRS, and SI models that are designed for specific diseases. Understanding the parameters of these models will assist us in maximizing their accuracy. For example, there is no explicit formula for the any of the rates within the models. Therefore, those rates must be approximated. Using these models to represent real world situations will explain why each disease needs to be represented by a specific model. Understanding the content and the rate approximations of each model can help to determine the level of accuracy the model will have in predicting the spread of the disease.
Cano, Christopher, "The SIR Models, their Applications, and Approximations of their Rates" (2020). Mathematics Senior Capstone Papers. 18.