Epidemic modelling for children
Description
It is argued that the fundamental science of an epidemic is that of one of the standard stochastic processes, one that should be familiar to anyone who has ever shuffled and dealt a pack of cards. An epidemic is modelled as a game of tag with two rules. A game of tag is modelled as a game of cards with two packs. For this minimal SIR model the act of tagging is seen to be 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. Textbook examples of a number of competing epidemic models which use different stochastic processes are listed for comparison. The Mathematical arguments contained in this paper are accessible from primary school to undergraduate levels. 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 may be interested after events of recent years.
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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