The minimal SIR model, validated then extended to social networks and stochastic differential equations

A discrete stochastic process which closely follows the mantra repeated duringCovid-19 about how epidemics grow is presented as a child's game of cards.When the results of multiple games are averaged the resulting differenceequations match the differential equations of thestandard SIR model and thus this minimal model is validated.Extending to an animal social network formed by voles allows comparison ofresults with those of the complete graph of the basic game.This allows questions to be asked about flattening the curve and seasonality.A discrete probability distribution for the ratio of growth to exponential growthis derived and seen to scale to the logit-normal distribution. Correlations forthe moments and underlying mean and standard deviation are then used to createa stochastic differential equation model.