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] from first principles.

The growth is determined by the hypergeometric distribution. As such the model debunks 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]