The card game

Epidemiology

Do you know how an epidemic grows? It's selection without replacement, thus sampling from a Hypergeometric distribution. Hence one infects two, two infect four or three or two or one or none. All with different probabilities and a weighted average of logistic growth.

This is deducible from a discrete stochastic process that was originally conceived as a game of tag and is so simple that a simulation can be conducted with just two packs of cards. The average being logistic growth means that the process forms a derivation of the standard SIR model [1] (corrected so that it is consistent with the definition of the basic reproduction number) from first principles.

The growth is determined by the hypergeometric distribution. As such the model supplants various stochastic models whether they have a normal distribution, use Gillespie’s algorithm or are based on the Reed-Frost model.

Being an Agent-based Model it can be easily extended. For example to a social network to show the effects of flattening the curve or of seasonality. [2]