Suppose is the number of turns which have been played in the disease game,
and is the number of diseased individuals in the th turn of the
game. Then one may write

where is the number of individuals which are newly infected during turn . A beginning model can be put together by assuming that the distribution of infective hexes and individuals creating them is random. If each infected individual `splats,' `sprays,' or `sneezes' into a zone covering hexes, and the board contains hexes, then an approximation for the total number of hexes which are infectious at turn is

The number of individuals which are still susceptible to being infected on turn , , is the total () less the number of currently infected individuals, that is

Then the number of new infections can be approximated

Putting this all together gives an initial, discrete logistic model for the propagation of disease:

In the case of the basic disease game, , (six hexes surrounding each diseased individual + the hex they stand in), and for the hex-grids provided. This model can serve as a foundation to build other, more advanced models from.

2000-07-28