With many sicknesses, MEASLES INCLUDED, you are contagious for DAYS before symptoms appear, as well as days after. Even if you are well-intentioned in your behavior, there is no way for you to prevent spreading the disease except for the vaccine.
Sorry it doesn't work the way you want it to work.
Absolutely true, and I don't deny the factuality of any of that, yet I fail to see the relevance. We don't deny people their rights on the basis that they might cause harm, even when there's a probabilistic reason to believe that they may do so. They need to actually do so first, or else demonstrate an intent to do so. I agree that we don't live in an ideal world where people are fully aware of when risks manifest themselves, but that is not an excuse for us to abridge others their rights.
Simply put, you are not harming only yourself with your anti-vaccine behavior. If you were, we wouldn't care.
I'm guessing you're using a generic "you" here, but just to be as clear as possible, I AM NOT AN ANTI-VAXXER, nor do I agree with their beliefs in any way. That said, I am a strong proponent of protecting our rights, especially when it is suggested that we remove them from people we vehemently disagree with, since I know that I could easily be the one in the minority someday.
(Plus, there's no punishment for people who do spread the disease like there is for people who act on their hate speech, and no way to enforce it once they get sick. So your analogy is not particularly relevant.)
Typhoid Mary was forcibly incarcerated for nearly three decades. HIV-positive individuals can face criminal charges for exposing or transmitting the disease to others. I'd say we have some case history for dealing with people who spread disease when they know better. But the lesson we can see in both of those cases is that even when people are infected, we still allow them to go out in public and enjoy all of the other human rights available, except, as I had said, inasmuch as it directly affects others. That someone poses an unrealized risk is, once again, not a reason to abridge them their rights. Mary was released after she agreed not to work in the food industry any longer, and was only detained again when she broke that agreement. And clearly we have few restrictions in place for HIV-positive individuals, though understandably the chance of transmission is lower with them than with an airborne pathogen.