I teach a Mathematical Modeling elective at the high school where Ben I. and I teach. I would love to do an in-depth object-based model using programming with my students, but generally speaking I don't have the ability to assume that all of my students know how to code. Most of them, but not all.
So, my solution is typically to use spreadsheets and the standard differential equation models to deal with disease spread. One of the simplest models is what's called the SIR model, which is an example of a compartmental model . Because these mathematical models are focused on total numbers in each category of the population and not on individuals, a spreadsheet is sufficient to see what happens.
Typically, for a three-compartment model, you need a minimum of three columns/variables to track overall counts. I would strongly recommend a fourth to keep track of time, and if you want, a fifth to keep track of deaths. You will need initial values for each quantity and parameters that are used to keep track of movement from one category to another.
For example, if I use the F1 cell to store the virulence parameter of the disease, F2 to store the recovery rate and F3 to store the lethality parameter, then we can build the model. I also recommend including a time-step parameter somewhere, let's say in F4. This will give you one control that will help to avoid calculation nonsense if some of your numbers are too large.
A B C D E F
1 Time Suscept Infected Recovered Dead virulence (1/1000000)
2 0 10000 1 0 0 recovery (1/100)
3 A2+F$4 B formula C formula D formula E formula lethality (1/1000)
4 c o p y t h e f o r m u l a s time step (0.1)
Where the B formula in B3 is =B2-F$4*(F$1*B2*C2)
Where the C forumla in C3 is =C2+F$4*(F$1*B2*C2-F$2*C2-F$3*C2)
Where the D formula in D3 is =D2+F$4*(F$2*C2)
Where the E formula in E3 is =E2+F$4*(F$3*C2)
Drag those formulas down as far as you want and make a scatter plot with all of the variable columns highlighted and you have a basic differential equation epidemiological model. It can be used to convey the very important fact that the most dangerous diseases to a population are the ones which are highly contagious, and not the ones that will kill you quickly, and that the ones which are highly lethal are actually safer for the population.
If you want other lessons from this, you're going to need to delve into the more complicated epidemiological models that demonstrate the effects of things like imposed quarantine, self-quarantine behavior, gathering of sick people at hospitals, vaccination, re-infection, or multi-stage diseases.