The point of liberty is for individuals to have the freedom to act of their own free will when such actions do not knowingly put other people in jeopardy.
To argue that people may not know they are contagious and since no one can tell if they are, they and everyone must be denied fundamental liberties is to condone totalitarianism.
Specific institutions such as hospitals need to figure this out. The general population does not. Rather, those afraid to get sick can isolate themselves. The rest must be allowed to live free lives until it is shown they are a health risk to others