A pretty good analysis here.

Public health issues involving compulsory measures divide conservatives and libertarians. They have for a long time. Do you have the right to go out in public after you know you have TB? Does the government have the right to compel vaccination against smallpox? What about diphtheria? Do you have the right to keep a bucket of stagnant water in your back yard? What about a fruit tree that you keep “organic” and which is infested with Mediterranean fruit flies? Does the state have the right to spray your organic fruit tree?

These are not trivial questions. They aren’t going to be settled here.