This is in fact the whole problem: "COVID could spread at a rate higher than 1 in schools, but if all teachers, parents and grandparents have been vaccinated (a

This is in fact the whole problem: "COVID could spread at a rate higher than 1 in schools, but if all teachers, parents and grandparents have been vaccinated (at a high uptake) then the spread in children won't spill into the older generations and therefore the overall reproduction rate might still be below 1." Yes, in this scenario the reproduction rate R could initially be below 1 making it look like we had herd immunity and could declare victory but it would inevitably increase to above 1, meaning an exponential growth in cases, even if all restrictions and everyone's behaviour was the same as when it was below 1. Here's why. Assume for convenience that Covid cases double each week in schools and halve each week in adults, there's no spread from one group to the other, and almost all cases are in adults initially. Initially we measure R and it's firmly below one, because almost all cases are in adults and those are declining rapidly. After one week there are twice as many cases in children and half as many in adults, after two there are four times and a quarter, eight times and one-eighth... and pretty soon the number of remaining cases in adults are so few any further reduction can't possibly compensate for the exponential increase in schools, and overall cases are growing exponentially and fast. Our declaration of victory was dangerously premature. The exact numbers don't even matter; so long as the reproduction rate is firmly below 1 in one group and firmly above 1 in the other, the group where cases are shrinking will make up an exponentially decreasing proportion of total cases and the overall rate of spread will quickly become determined by the group where cases are still growing. (The assumption of no spread from one group to the other doesn't matter either; it just makes the explanation slightly simpler.)