Thanks, Jim. These fall into the category known as compartment models ([wikipedia](https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology)), which are essentially stochastic models of data flow along a directed graph. SIR models give a transient notion of patients that recover, which is also an important consideration.

> ![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/32/Sirsys-p9.png/330px-Sirsys-p9.png)

> ![](http://imageshack.com/a/img923/5330/2oBS7s.png)

>Blue=Susceptible, Green=Infected, and Red=Recovered, for the directed graph shown below the chart


From our book, a short appendix on compartment models is available for free (another medical application is on pharmacokinetics, which is how one models drug delivery) : https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/9781119434351.app5

Compartment modeling relies extensively on the concept of convolution, which can be calculated easily via a scripted software algorithm, described in another appendix
https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/9781119434351.app2

There's unfortunately no convolution operator built into the Excel spreadsheet, but there's a nifty array-syntax trick that allows you to calculate a convolution between two ranges very compactly. If anyone is interested, I can describe exactly how to formulate an Excel convolution.

BTW, compartment modeling is the basis for our comprehensive Oil Shock Model, which I think will also be an important model in the near future, as it will help to understand the sharp disruption in global oil production that will eventually impact the world, see our blog https://peakOilBarrel.com for up-to-date projections. The Oil Shock Model is described in Chapter 5 of the book (which is behind a firewall):
https://agupubs.onlinelibrary.wiley.com/doi/10.1002/9781119434351.ch5