See here. Very strange.
The most important fact we see is that for people over 50, the most dangerous period after vaccination is between 6 and 9 months after their last dose. Their risk of hospitalization is several times higher than before six months or after nine months. The increase in risk far outweighs a small reduction in the first six months.
As a side note, this chart shows that additional boosters outright do not reduce risks for people under 50. However, those have very few hospitalizations, making the data less reliable for those ages.
So, people who take a Covid booster first go through a somewhat reduced hospitalization risk for the first six months, then go through a dramatically heightened risk of hospitalization, then hospitalization rates “return to normal,” with the normal being very high. Does that look like the vaccine provides any benefit? Not to me!