That leaves herd immunity. Epidemiologists tell us it requires between 60 to 80 percent of the population to have antibodies. At the moment, though, lack of testing means we don’t have a clear picture of the spread of the disease; a generous rough estimate for how many Americans have been exposed is 5 percent. While there are some reasons to hope that the exposure could be significantly higher, 5 percent would be more than ten times higher than the number of known cases, and would be in line with large-scale serological surveys in Holland (where the disease has been relatively widespread), suggesting that 3 percent of the population had antibodies. Others projections suggest that the U.K. is only 5 to 6 percent through the course of its pandemic, and recent models estimate an immunity level of about 6 percent across seven European countries. And it means, taking that generous figure for disease exposure and the low-end threshold for herd immunity, we would need 12 times more exposure than we’ve had to this point — in other words, that we are only one-12th of the way through this crisis.

That may sound bleak, and there are some indications that the population spread could be much more broad. But assuming no wild underestimate of total asymptomatic cases, one-12th of the way through the crisis is a very optimistic projection, if not quite a best-case scenario. It is possible that even less of the public has been exposed — perhaps one percent or lower. At that level of exposure, we could be only one-80th of the way through the pandemic, requiring 80 times more infection and exposure to attain herd immunity than we have had to this point.