The computational SIR model

The SIR model is popular compartment model with three populations, the susceptible, infectious, and recovered groups S, I, and R. It characterizes infectious diseases that provide immunity upon infection. Since the SIR model has no analytical solution for the time course of its populations, we discretize it in time using finite differences and adopt explicit and implicit time integration schemes to solve it. We compare the timeline of the SIR model to the analytical solution of the SIS model and show its sensitivity to the infectious period, reproduction number, and initial conditions. To illustrate the features of the SIR model, we simulate the early COVID-19 outbreak in Austria using reported case data. The learning objectives of this chapter on computational SIR modeling are to