Using physical simulations to motivate the use of differential equations in models of disease spread

Abstract

The SIR model is a differential equations based model of the spread of an infectious disease that compartmentalises individuals in a population into one of three states: those who are susceptible to a disease (S), those who are infected and can transmit the disease to others (I), and those who have recovered from the disease and are now immune (R). This Classroom Note describes how to initiate teaching the SIR model with two concrete physical simulations to provide students with first-hand experience with some of the nuanced behaviour of how an infectious disease spreads through a closed population. One simulation physically models disease spread by the exchange of fluids, using pH to simulate infection. A second simulation incorporates randomness through the use of a probability game to keep track of the state of each individual at each time step. Both simulations invite students to ask questions about what factors influence disease spread. The concrete experience from the physical simulations enables students to make connections to the abstract mathematical representation of the SIR model and discuss the sources of stochasticity present in the spread of an infectious disease.