A trespasser is an "ethical subject", somebody capable of taking rational actions, thus somebody with rights, and by extension, somebody that must respect other people's rights and should be deemed responsible if s/he doesn't. A disease is not a responsible, rational being.

Let's put it in another way: imagine you have a restaurant, and without noticing it you serve rotten food to a client. The client gets sick. I consider you to be responsible. You can't blame it on the bacteria that "invaded" the food.


Not that "immediately", of course. Even if something is considered to be a violation of the NAP, there are several justice principles, like proportional punishment, presumption of innocence etc. These principles would render such scenario quite rare. For less dangerous diseases, nobody would bother searching a "guilty" transmitter, because even if you do find it, any applicable punishment would likely not pay for the trouble. And even for serious diseases, you'd need to prove that it was person X specifically that passed it to you.
That's why I don't think that, in a free society, people would manage dangerous transmittable diseases this way. It would likely be something closer to what Robert Murphy describes in the article I linked above: people using their discrimination rights to block sick people from their properties.