Unlike most medical interventions, vaccination is not about one's individual well-being, but more about the protection of the entire population, especially other, more vulnerable individuals (https://en.wikipedia.org/wiki/Herd_immunity).
This is why some vaccines are recommended even if you're not especially in danger, because they help protect others that may not be able to be vaccinated (because they are too weak, or due to a special reaction to the vaccine etc.)
Not saying that it means that forced vaccination is morally justified however! But the question of vaccination is definitely not simply about individual choice in regard to one's own health.
The question isn't 'can we rationalise this?' - we can rationalise everything. The question is 'is the threat great enough for the government to start infringing on liberty?'. It probably isn't, otherwise we'd ban all hard and soft drugs (including alcohol & smoking) as a similar level of threat to public health. That battle has been fought and lost by the public safety folks.
An incentive program would probably be a good idea, but I expect there is already one in place.
It’s all about managing th externality.
I think that’s over the top. The most legitimate argument for forming governments is the management of externalities. It infringes on the factory owner’s liberties to restrict their dumping of toxic waste into the river.
Likewise vaccines and quarantine are ways to limit the spread of dangerous pathogens.
There are no real negative effects for vaccination, as long as you don't force them on people who have genuine medical conditions preventing them from taking them safely (e.g., allergy to vaccine components).
Also, an interesting note: if you join the military, you have to get vaccinations. You're not allowed to opt-out.
So no, cost is not the reason and I think it's a bit scary that that's the best reason you could come up with.
I'm as sceptical of antivaxxers as most of HN, but I'm appalled at the level of support for forced medical intervention in the comments here. That's the stuff of dictatorships.