The SIR Model

The SIR model is defined by the following ordinary differential equations.

β/N * I * S describes how many susceptible move to the infected group. A susceptible person (S) has to meet an infected person (I) and the rate of transmission when such an event occurs is beta. beta is scaled by N, the total population size (N = S + I + R).

γ * I describes how many infectious individuals move to the recovered group. gamma is the recovery rate.

We can implement these equations in a coding language, for example R or python (we chose R here), and simulate the model over time and investigate the trajectory. For the simulation below we chose the transmission rate β = 0.5 and recovery rate γ = 0.1 (Fig 19).

In this example (Fig 19), we defined the number of the susceptible at the beginning S0 as 1999 and the number of infectious people I0 as 1. We chose beta as 0.5 and gamma as 0.1. We then ran a simulation, meaning that we ran the model using these values, to see what a pandemic under these conditions would look like. (For those interested in how to implement SIR models in R, please refer to this: http://rpubs.com/choisy/sir)

Let’s try some activities now to test your learning about the SIR model:

Go back to our initial question that we raised previously in the introduction – Why do modelling? – and see how they apply to the SIR model. Now, test your learning by going through the activities in the following pages.