it seems like you cannot swing a sack of desperate epidemiologists around your head these days without hitting another “model” claiming that “vaccines saved upmteen squinjillion lives” but i fear these these weapons of mass deception are just overwrought GIGO engines that run on bad assumption, bad data, and worse study design/definitional hijinks.
but there is a simple truth test to these matters: if these vaccines were anything like as efficacious as claimed, dosing them into 70%+ of populations (and 90-95% of high risk of death populations) then they would be bending the covid curves like neutrons stars bend spacetime.
the effects would not be subtle.
And rest assured, the "bends" we now have are not going go away any time soon.