ROME — There is a growing sense in Italy that the worst may have passed. The weeks of locking down the country, center of the world’s deadliest coronavirus outbreak, may be starting to pay off, as officials announced this week that the numbers of new infections had plateaued.

That glimmer of hope has turned the conversation to the daunting challenge of when and how to reopen without setting off another cataclysmic wave of contagion. To do so, Italian health officials and some politicians have focused on an idea that might once have been relegated to the realm of dystopian novels and science fiction films.

Having the right antibodies to the virus in one’s blood — a potential marker of immunity — may soon determine who gets to work and who does not, who is locked down and who is free.

That debate is in some ways ahead of the science. Researchers are uncertain, if hopeful, that antibodies in fact indicate immunity. But that has not stopped politicians from grasping at the idea as they come under increasing pressure to open economies and avoid inducing a widespread economic depression.