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This post demonstrates the dynamics involved in a susceptible, infected, and recovering (SIR) model previous post for the model.  The shiny ui and server code can be found on GitHub.
of dynamic programming.

As a dynamic infection model, I find it particularly satisfying to be able change parameters and observe instantaneously changes in predicted outcomes.

This is a very simple model.  However, there
are many interesting models feasible that use this basic structure.  A more involved though fundamentally no more complex model might consider a simulation in which there are multiple sub-populations with different contact rates and transmission rates.  How might an optimal intervention be positioned in order to minimize total population exposure?

You can experiment with the app yourself at:

http://econometricsbysimulation.shinyapps.io/Dynamic-Pro