R number only as good as current cases of infection, right?

[AdultHumanFemale]

Help me clarify, please.
A relative is thrilled the R rate is down and thinks this means restrictions will soon ease as a result.
I am thinking that, as the current number of new infections is still very high, a lower R number doesn't mean that the number of cases in the community is equivalent to when the R rate was at a similar number low last year. The R is relative to the current number of infected persons, right? DRel is having none of it.

The R rate simply refers to the number of people each infected person is likely to infect. It has no relation to the overall number of people infected at one time.

An R rate below one means each infected person will on average infect less than one person (in reality of course what actually happens is some people infect no-one and some several, which averages to under 1 per infected person) so the pandemic starts to decline. It doesn't say anything about the overall number of infected (could be 1,000, could be 1,000,000!).

So the R rate being the same as it was in say June doesn't mean we can behave as we did then, because far far more people have it now and it will take quite some time for absolute numbers to decline.

You are right

If R is 1 then the number of cases stays the same because it means overall one infected person passes it on to one more (obviously that means many people pass to none, some pass to many, but it evens out at 1)

Higher than 1 and the number of cases rises, as overall,each person passes it to more than one person (can be a fraction, as it might be the case that every 2 people wouid pass it on to 3 people)

If it is less than 1, then the number of cases declines, but it does so slowly. Say it's 0.8, that means that 40,000 cases (roughly today's figure) produces 32,000 new cases - still way too high. The decline will be slow, because we cannot sustain that number of new infections and the expected number of hospitalisations it brings.

We need to get the transmission really low (anyone got any idea what sort of figure?) so that hospitals can empty out before seeing if we can safely relax any restrictions without filling hospitals again. Ideally with NHS staff getting a break - though of course they will be under considerable pressure to tackle backlog as quickly as possible.

This is what I have been trying to explain. I can't see how I can make it clearer, and I teach primary school so am used to breaking things down Until now, I haven't met anyone who seems to be invested in deliberately misunderstanding what they hear, but I think this might be what is happening...

R number alone isn't going to ease restrictions but R number has to reduce for infections to reduce then when transmission is low enough we should see some easing of restrictions. So it won't happen straight away but it is a sign we are heading in right direction.

As new varient spreads more easily I assume numbers have to be even better and restrictions easing more gradual than last time too.

The thing is that when you relax restrictions R will go up and, if it's above 1 at that point cases will start to increase again. But the number of cases at the end of lockdown will affect where on the curve you are things start again; are you starting from the flattish bit of the exponential growth curve or near the top. Say R goes up to 2 post lockdown, so each new case affects 2 people, and you exited with 10 cases, you end up with 20 new cases. If you're on 10,000 cases when you exit you can expect 20,000 new cases.

You also need to factor in daily cases. At the end of the summer we were c. 1200 cases per day. Nothing like where we are now.

What do they think R means? Do they understand that the R is nothing to do with the virus’s characteristics, but it’s all about how many people each infected person infects under the current restrictions. It depends on

a. the number of interactions between people.
b. the number of people with the virus

Currently we’re relying on a. being low because b. is still high. When b. is low (and can be kept low because of the vaccines), a. can be increased carefully.