Infection numbers in the countries Michael names do seem to be levelling off – (Caveat: it’s a bit early to say) – but maybe vaccination is not the cause, or not the only cause. Take a look at the global Daily New Cases graph (as always, tick the box and look at the “7-day moving average”):
https://www.worldometers.info/coronavirus/
Numbers are still rising, but the rise started slowing down around eight to ten days ago. So how is vaccine rollout globally? My guess is, not enough to be the cause of that slow-down.
If we don’t know what’s slowing it down, we don’t know what might speed it up again.