I tried modeling infection rates, number of infected, and total number recovered and dead. Couple of things stood out.

1. Reducing the transmission rate lowers the total number of people sick at one time. Lowers the ultimate number who contract it. And pushes the peak infection rate out.

2. The above numbers are very sensitive to r0.

3. An exponential when it hits looks like a wall. You end up with a significant percentage of the population sick at once.

Could be my model being shitty but it looks like at high r0 there is a momentum effect which drives the total number infected above what you would expect.

You’re describing a typical SIR model (susceptible infected recovered) which can be solved analytically. You can see the dependence on all those points you mentioned above.

Note this is a “mean-field” model (everyone evenly mixed together) so take it with a grain of salt...

That's what I was trying to do. I thought it would be interesting to build one and play with it. The issue with it being a mean model vs a mixes contact model noted.

Both of these models are well studied and compared in the literature

This website doesn't contradict anything I've said and I cannot see the relevance to the point.