User:Zebmason/sandbox

Epidemiological tag is a tag-based game that is also an example SIR model. The growth of an epidemic may be explained as one person infects two, then those two infect four others. Alternatively the two try to infect each other and the first person and the epidemic halts. i.e. An epidemic is a stochastic process rather than deterministic.

The rules
Players are in one of three states
 * Susceptible - never been tagged
 * Infected - tagged and haven't yet passed the tag on to two others
 * Recovered - have tagged two others, won't tag any more but can be tagged again

Initially all players are susceptible except for one who is infected.

An example game
A game was played with 31 players, starting with player A the game proceeds to build a directed graph with the exception of 4 players who've never been tagged thus demonstrating herd immunity.

To make sense of this tangle the subgraph formed by the edges corresponding to the first time a player is tagged is constructed.

The number of individuals in a column can be used to construct a plot of the infected showing divergence from exponential growth before a peak and then a decline.

Then summing those numbers constructs the plot of the recovered, resulting in a sigmoid curve.