26 Card Epidemic

This is introduced in Epidemics: Mathematical Models.

Equipment required: a pack of cards (no jokers), record sheet

  1. Sort your pack of cards into 26 red and 26 black. We only care about colours for this so the suit and number don't matter. Red are going to represent both susceptible people (when they are face down in the population) and infected people (once picked). Black cards represent immune people.
  2. Put the pile of black cards to one side, face up. They will be used to replenish the population later. Put the pile of red cards face down.  This is your population of size 26. This pile must always have 26 cards in it.
  3. Start the epidemic by picking one from the population (the 26 face down cards). Of course it is going to be red, so it represents the first case. Put the card on the table face up and then put a black card into the population pile to indicate that that person can't be infected again.
  4. Now repeat steps 1 to 7 below until there are no new infections (ie. you pick all black cards) or you run out of cards:
    1. Shuffle the 26 card population.
    2. Count how many infecteds (red cards) you had the previous round and double it.
    3. Take that many cards from your population.
    4. If any of the cards you have just picked are black, put them back into the population pile, as they are resistant to infection. Red cards indicate people who become infected this round.
    5. Put infecteds on the table in a new pile next to the previous round.
    6. REPLENISH the population with as many black cards as there were red cards.
    7. Add a point to your record, so that you produce a graphical record of the progress of the epidemic.
  5. When the epidemic has ended (all black cards picked), record the total number of people infected.

Things to think about:

  1. What does it mean for the population that we keep it at size 26?
  2. What patterns are you seeing? Think about the initial steps, the overall shape of the graph, the duration and any variability.
  3. What is the probability of no one being infected at step 3? (Step 1 is the first infected person.)
  4. How might things change if…
    1. you started with more than one infected person?
    2. you had more cards?
    3. each infected person passed on the disease to a different number of people?
  5. Is this a realistic model? What is missing, and does it matter?
  6. How could you change this model to be more realistic, and what effects do you predict it would have on the epidemics?