“The medium term is going to be particularly perilous,” said Nada Sanders, a professor of supply-chain management at Northeastern University. “Global demand is so high, and supply is so far behind, that it’s very hard to envision enough of a ramp-up.”

“Even for diseases we’ve been studying for over 100 years, like whooping cough, we still don’t know what level of antibody would indicate that you’d be protected if you got reexposed,” said Sam Scarpino of Northeastern University, who studies infectious-disease dynamics. The only way to find out is through long studies.