Modelling an epidemic exercise

This exercise demonstrates a simple modelling principle similar to those used as the basis for modelling the COVID-19 pandemic.

You need a pen and paper, and two six-sided dice (or virtual dice).

  • On your paper, draw a table with six rows, one for each number on the dice, and plenty of columns. The rows represent our population — six people who may catch the disease.
  • In the first column, write a letter ‘I’ in the first row, and a letter ‘S’ in the other five. This means person 1 is ‘infected’ — patient zero of our simulated epidemic — while persons 2 to 6 are ‘susceptible’ — they’re healthy, but can catch the disease.

Now play the game with the following rules:

  • Toss the two dice together. If one of the two numbers corresponds to a person who is ‘I’ in your table and the other number to an ‘S’, the ‘S’ person will become an ‘I’. This represents a random meeting, in which an infected person spreads the disease to someone else.
  • Hold this result in your head and toss just one dice, if the number that comes out corresponds to an ‘I’ person, they become ‘R’, meaning they’re ‘Recovered’ from the disease, and are now immune.
  • After each two throws (of two and then one die) fill in the next column of the table to show your results.
  • Repeat the turns until there are no more ‘S’ people, then count the numbers of S, I and R for each column.

Unless the simulated people in your table were really lucky (it can happen, with so few of them), you can see how the number of ‘Is’ increased with time, as the disease spread. They reached a peak, and then went down again, because all the people they met were already immune. You can plot it in a graph like this:

 

 

 

 

 

 

 

This is a toy version of the so-called ‘SIR model’, the simplest model of epidemics. The Imperial College model is based on a similar concept, but is of course much more elaborate.

If your six dice-people started social distancing, infections might become less likely. You could for example toss another dice to check if an infection really happens when an S meets an I (assume it happens only if you get a result below a 4. If not, assume the infection recorded by the first throw did not happen because although they met, the susceptible person did not catch the infection). That will flatten the curve, or even kill off the epidemic entirely.

Real-life models account for many more possibilities — different severity of infection, different ages of people, the possibility that immunity does not last, the risk of death. And they draw their probabilities from studying the disease in the real world, and using the actual data. But at their core is a strikingly simple idea.

Simone Sturniolo