You're putting words in my mouth. "Public health" deals with social problems regarding health, but it's a subset of "health" which also includes problems that are not social in nature.

There are absolutely social issues around vaccines — how do we fund their development? how do we distribute them? how do we convince people to use them? — but as a technology I would say they solve a problem that is mostly independent of human relationships.*

* Obviously, you could say that vaccines actually do solve a social problem because pathogens are often passed between humans, but I think then the definition of "social problems" becomes so broad as to be meaningless.