And so they aren't still counted. So in my example you had 200 people to start with, 220 new people are infected and the initial 200 either died or got better.The recovered or dead don't (re)infect anyone.
You were wrong in every single way possible.Ok, please explain.
You either have 320 people infected by 200, which gives you an R of over 1.5, or you've included the initial batch which means you haven't waited a full cycle.
You've also assumed that the testing has magically gotten much better at finding the infected people. From starting with 50% detection and going to either 100% or around 70%. All told, just wrong.
Now that's a good question. There are tests done each week, similar to how you do polls for elections of people. Those are used to estimate the number of cases in the UK. Note that these are separate to the normal testing stream. When you have an idea how many people are infected each week you can work out what the R value is, roughly.Also - how an R number can be determined when it is not known how many have the virus.