Mathematically speaking this is a discrete markov process. If you study the continuous version of these type of systems then by only given the rates you can prove what the eventual behaviour of the system is (from a measure theoretical perspective) . I guess your system is a just a contact process -> See 1.3 over here http://staff.utia.cas.cz/swart/lecture_notes/partic17_04_07.pdf over here.
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Shh... I had that planned for another post to explain this system mathematically and nobody was supposed to know that yet!
Just kidding about the nobody was supposed to know part. I will definitely use that as another source when referencing the other post, though how it explains it in your resource is slightly different than how I had always seen the contact process explained (in other sources from reading up on it) so I still kind of learned something. As well mine is slightly more complex than just a simple contact process as it has both the vaccination rates and the infection rates and whether someone is vaccinated or not will affect the rate of spread of the infection along with some other things but still you are correct! I wish I could vote you for more.
Yeah it is a bit different from an ordinary contact process.
The theory for these kind of stuff that I am familiar with hold on lattices of the type
. Which is in some sense a lattice on 
So it might be fun to explore what kind of results you get if you implement this kind of stuff on a torus.
I could check it out and try the implementation though I am unsure about pygame in its ability to handle the 3rd dimension. I mean python already does O(nlogn) algorithms as O(n2)
So I will definitely look into it but it might take a little longer to implement this into 3d (for application) than it did for 2d
I mean a 2d torus (S x S). By identifying the opposite edges on a square you can create a torus.
Yes but it would be prettier to look at if it was a complete torus, as well I can just write it in C++ and have it work a lot faster