Take a look at this story that ran on the BBC today: Covid: Israel's vaccine rollout linked to infection fall. There is some remarkably good news from Israel, which have already succeeded in vaccinating half (!!) of their population.
Israel's vaccination programme is showing signs of working to drive down infections and illness in the over-60s.
The fall appears to be most pronounced in older people and areas furthest ahead in their immunisation efforts.
This suggests it is the vaccine, and not just the country's current lockdown, taking effect.
There are lots of details in the linked article.