Epidemic modelling for children
Description
An epidemic is modelled as a game of tag with two rules. For this Minimal SIR model the act of tagging is seen to be the well-known stochastic process of selection without replacement. Averaging the associated probability distribution results in the logistic growth term of the Standard SIR model with a slight correction to be consistent with the definition of the basic reproduction number. Being an agent-based model it is easily extended from the complete graph to social networks leading to a flattening of the curve with far fewer individuals having acquired immunity by the end of the epidemic. Arguments are given as to why this model supplants the chain binomial model and stochastic variations on the Standard SIR model such as Wiener processes and Gillespie's algorithm. The Mathematical arguments contained in this paper are accessible from primary school to undergraduate levels, the game itself can be recast as a card game for those unable to run around. The decreasing probability of the game matching exponential growth can be calculated in a manner similar to the solution of the Birthday problem. There are also difference equations and differential equations making this theory a rich and varied example for teachers whose pupils will hopefully be interested after events of recent years. Finally, this simple model should hopefully supplant the simplistic model of exponential growth which people are prone to parrot in defiance of the prior art since 1840.
Files
minimal.pdf
Additional details
Software
- Repository URL
- https://stochanswers.com/education/tag.html
- Programming language
- JavaScript
- Development Status
- Active
References
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