Percentage of population innoculated for spreading to stop

Please take this down if Covid questions are frowned upon.
A question to the modelling cimmunity though. I have been trying to figure out what percentage of the population needs to be innoculated before Covid will stop spreading.
In the UK we started the first dose of vaccines in December. We had a worryingly high peak of cases which is not going down. The R number in my area is 0.8 I believe.
How do you assess the percentage of the population who need to take the vaccine?

I would say it’s dropping quite fast

My apology - I mistyped. ‘which is going down’

This is actually a much more complicated question than it seems. If you model a simple differential equation system, in which there are no “individuals”, but continuous fractions of sick, immune, and susceptible individuals, the spreading never stops. The fraction of sick individuals tends to zero, the fraction of immune individuals tends to 1.0, and the fraction of susceptible individuals tends to zero.

To perform a good estimate of the fraction of individuals that need to be immune to stop spread, one really needs to know the distribution of the individuals in space and their mobility. Thus, realistic modelling of such a thing depends on an actual representation of the distribution of people in your country/region and how people displace and interact.

Extreme cases illustrate this situation: if the only sick individual is completely isolated until recovery or death, nobody else gets sick, and the fraction of immune individuals to stop spreading is zero. If a single individual is initially sick but enters in contact with thousands of people every day, and these people also do not isolate, probably everyone will eventually get the disease, no matter which fraction of the population is immune already.