Sanitation is a problem for one person as well, as is health. Social problems arise specifically with the interaction of two people. You can't have a scam without two people, for instance.
Definitions that collapse the entire space under discussion into one category are useless. If sanitation is a "social problem" then everything is a social problem, and the reason why that is useless is just that a definition that does not distinguish has no utility. In mathematical terms, to say that something conforms to that definition yields zero bits of information. "Public health" is its own category. In the real world no two categories can ever be fully separated from each other but just because plausible scenarios can be spun out in which sanitation becomes involved in a social problem doesn't mean that on the whole it is much better understood and talked about as a separate category.
Crypto has social problems. If one person sits in a basement and "does crypto" by themselves who cares? They can declare they own as many basement-coin as they like. It takes a second person to have a problem.
Social = society, keep that in your head.
The vast majority of problems you are going to face in your life are social problems because you live in a vast interconnected society with millions/billions of other individuals.
And it is important to remember that almost all problems are social problems, we get a quite a few of the libertarian types on HN that think "I'll just ignore other people and now I've solved every problem in the world". It's why this group of people thinks this way, it makes the problem way easier if you ignore reality.
Money, and the assorted scams around it, regardless of what type of money it is, is a social problem by definition.
You see this a lot from people who have been lucky enough to live in places where problems get addressed somewhat automatically. When you spend enough time in places where that isn't true, you quickly realize how indoor plumbing - or almost anything, really - becomes a social problem.
Health: If your neighbour has a contagious disease, that is going to be an issue for society as well.
Are we going to pretend that COVID as a problem doesn't fit your chosen definition perfectly: "two people to have it, and that they must have it in relation to each other, which is to say, some sort of social interaction or communication must be involved as well."
Sanitation and health are social problems because if they are not handled they have an extreme effect on society in general. Hell, for plumbing we ONLY care about it as a social problem. If you go live somewhere far enough away from people, we don't care if you shit in a bucket. If you live in a city, we absolutely care about the social effects of not having sufficient plumbing.
If my neighbour has a broken TV, that's a problem that will never affect society. If my neighbour has a contagious disease, or even a non-contagious condition, there are a LOT of ways that affects society.
Same with a neighbour with plumbing that isn't up to code. There's a reason we send government agents in to verify plumbing installations, but we don't give two shits about your TV setup.
I suspect that anyone that says that plumbing or health is not a social problem is living in a place where those things are handled well enough as a social problem that you have never seen what happens when they aren't handled.
I think it's reasonable to say that a problem is a social problem to the degree that its severity as experienced by one person depends on other people's behaviour.
If I accidentally drop a rock on my own foot, this seems to be obviously not a social problem. But if I am more likely to be carrying a rock in the first place, or less likely to be wearing protective shoes, because of how society is organised, then to that extent I claim that it is a social problem. This is not an abstract example: Over time, changes in society's attitudes to dangerous kinds of work have directly, and indirectly through health and safety legislation, led to massive reductions in workplace harm since the Industrial Revolution.
Under this rubric, all it takes for a problem to be social is for it to be possible to imagine that society being organised differently would lead to a different level of suffering. Does this lead to nearly all problems being classified as social problems? Yes -- but that is not a problem in itself, that is just an accurate picture of reality! It is still useful -- indeed much more useful -- to place problems on a spectrum of social-ness; nothing "collapses" unless we are determined to make a black-and-white distinction.
If my neighbour has a "removing raw sewage from living spaces" problem, it is very much a concern for me.
If my neighbour can't watch TV, I don't care.
TV breaks because entropy doesn't like you = personal problem.
TV breaks because manufacture designed it to fail 3 months after warranty = social problem.
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.
"how do we stop dying from pathogens" is like, the textbook public health problem. it's pretty much the question which the entire concept of public health spawned from.
so, if you specifically wanted to talk about the technology of vaccines or whatever instead of general pathogen prevention, you should just say that instead. i cant read your mind.