SIR Model

Susceptible – Infected – Recovered

The SIR model uses three groups (or compartments):

  • Susceptible – Those who do not have the disease and thus can be infected.
  • Infected – Those who currently have the disease and potentially may infect others
  • Recovered – Those who have had the disease and are now recovered and thus not able to re-catch the disease (at least for a period).

The groups are often referred to as S, I, R for short, but beware ‘R’ also has another meaning, the ‘reproduction number’ (see below).

When the disease can be fatal, the ‘recovered’, category includes those who have died with the disease; for this reason some people refer to the last category as ‘removed’.

The model is driven by a number of parameters:

  • alpha – the transmission rate, that is the number of people per day that potentially catch the disease from an infected person, assuming they are susceptible.
  • beta – the proportion of infected people who recover each day. For the purposes of this model deaths are treated the same as recovery, someone who cannot catch the disease again.

For these we can calculate:

  • The average time a person stays infected is days.
  • The reproduction number (also called R), “the average number of secondary infections produced by a single infected person” ( is the reproduction rate the average number of people who catch the disease.

We’ll start with a total population of and initially infected people.