To describe a system in an exact language

Instead of simply stating “the number of infected people will increase if more people are infectious”, the SIR model expresses this relationship as: the rate of new infections depends on how many people are susceptible and how many are currently infectious. This relationship is captured mathematically and can be explored and tested, helping to remove guesswork and make reasoning about the system more rigorous. Moreover, the SIR model can be very useful to:

• Discuss what the crucial components or processes in a system are
• Identify assumptions
• Identify what is missing in a discussion

It is generally a good idea to begin with a simple model and extend it as more information becomes available. During the COVID-19 pandemic, many research teams used the SIR model as the foundation for their model development. However, it soon became clear that there is a delay between the time a person becomes infected and the time they themselves become infectious. The SIR model can be easily extended with a compartment for the “Exposed” (E) to represent this process. In the resulting SEIR model, individuals move from susceptible (S) to exposed (E), and then from E to infected (I). Similarly, it became evident that people could be reinfected with COVID after some time due to waning immunity. The SIR model can be further extended to include a transition from the Recovered (R) compartment back to S; this variation is typically called the SIRS model. Both processes are represented in the SIRS model.