But anybody licensed to practice has spent a lot more time studying medicine that your average coder or engineer. Among the matters they have studied is the current best understanding of vaccines. It isn't the guy last in his class who's coming up with the recommendations that the others follow. And what's best for you in your narrow little case is very likely most of the time what's best for the "herd".
A huge amount of research into how vaccines are deployed is, and is done by, people with skill in applied mathematics.
You have undoubtedly met fewer doctors and fewer coders and engineers than I have. (I'm older than most people on HN.) Anyway, IQ is not the relevant issue. The issue is specific training and clinical experience. For equal IQ scores, I will ask engineers to solve my engineering problems, and doctors to diagnose and treat my diseases. If each professional has passed the required training course and has continued in practice with a license with good reputation, I don't need to ask IQ scores before I seek a doctor or seek a coder. What's important is getting the work done right, and doctors have better background for doing medical work than engineers or coders.