That’s two days in a row with a study suggesting greater prevalence of coronavirus within a particular population than one might expect. Yesterday doctors in a NYC hospital reported that 15 percent of women who gave birth in their care during late March and early April tested positive for the virus. Of that number, 88 percent had no symptoms.

Today there’s a new study out of Boston, this time of a population of homeless people. Result: An even greater prevalence of COVID-19 but still the same large share of asymptomatic patients.

One of the key unanswered questions in the obstetric study remains unanswered here too, though. How many of these people never had symptoms and how many went on to have some after they were tested? Everyone infected with the virus is pre-symptomatic at some point. What we want to know is how many remain asymptomatic throughout their infection.

Fully 83 percent of those at the shelter who tested positive had no symptoms, in line with the share of infected pregnant women. Note too that both the New York tests and the Boston tests were done via PCR, i.e. the nose/throat swab that detects whether the virus is present in the person *at that moment.* Conceivably, some members of each group had already had the virus and recovered, clearing it from their system before the PCR test was done. Detecting that would require an antibody test. If we’re looking for evidence that many more Americans have had the disease than thought and most didn’t even know it, that’s something to consider.

Another question raised by both studies is how representative they are of the total U.S. population. I floated a theory yesterday for why pregnant women might not be a good yardstick for the average American: They’re visiting doctor’s offices more often than most people are during the final stages of their pregnancy so they may have picked up the virus there. (There may also be immune complications from pregnancy.) It’s easy to see why the homeless might not be a good yardstick either. In cramped quarters like a homeless shelter, the virus may spread like lightning. Even outside the shelter, the homeless don’t have the luxury you and I do of hunkering down in a private space. They need to panhandle or visit soup kitchens to eat, where they’re bound to end up in close contact with others. Poor nutrition, and poor health generally, doubtless has an effect on immunity too.

On the other hand, the fact that only a small percentage of a vulnerable population like the homeless were symptomatic — at least at the moment they were tested — is encouraging for those of us who want to believe the disease is more common, and much less severe, across the entire population than the current gruesome spike of cases in NYC and elsewhere suggests.

But let’s not get our hopes up. Doctors in Iceland have been seeing cases in their country since late February and by mid-March were testing the population, both those who seemed at special risk for infection and a random sample of people to see how far it might have spread. The result wasn’t encouraging for true believers in the Oxford model of the epidemic.

As of April 4, a total of 1221 of 9199 persons (13.3%) who were recruited for targeted testing had positive results for infection with SARS-CoV-2. Of those tested in the general population, 87 (0.8%) in the open-invitation screening and 13 (0.6%) in the random-population screening tested positive for the virus. In total, 6% of the population was screened. Most persons in the targeted-testing group who received positive tests early in the study had recently traveled internationally, in contrast to those who tested positive later in the study. Children under 10 years of age were less likely to receive a positive result than were persons 10 years of age or older, with percentages of 6.7% and 13.7%, respectively, for targeted testing; in the population screening, no child under 10 years of age had a positive result, as compared with 0.8% of those 10 years of age or older. Fewer females than males received positive results both in targeted testing (11.0% vs. 16.7%) and in population screening (0.6% vs. 0.9%). The haplotypes of the sequenced SARS-CoV-2 viruses were diverse and changed over time. The percentage of infected participants that was determined through population screening remained stable for the 20-day duration of screening.

I’m open to theories that Iceland is unrepresentative of other populations. Certainly their climate isn’t helping them to keep the virus at bay, though, as temperatures were in the 30s and 40s during March. If the virus spreads like wildfire, infecting many more people than scientists think, why is prevalence in Iceland below one percent? Did they simply test “too early,” before exponential growth had time to work its magic?

If you’re excited by the New York and Boston results, stay tuned for a much more representative population study courtesy of, uh … Major League Baseball.

About 10,000 employees from 27 of MLB’s 30 teams are being tested to detect whether they have already contracted and potentially recovered from the coronavirus. Participants span the organizational payroll, including owners, front-office executives, scouts, stadium ushers, hot-dog vendors and, in some cases, the players themselves…

The doctors involved said that a study of this nature typically would take a year or more to complete. With MLB’s help, the process is already near its conclusion after about a month. Pinprick blood tests, to be self-administered by employees at their homes, generate a result within 10 minutes and should be completed by the end of the week. Dr. Bhattacharya said he plans to write a paper over the weekend and send it out for peer review.

“If you don’t know how far along the disease is we can’t do good forecasts,” Dr. Bhattacharya said. “If we can’t do forecasts we can’t understand when it’s safe to open up the economy.”

Bhattacharya has been skeptical since the start that the virus is anywhere near as deadly as many scientists fear. He suspects, as the Oxford researchers do, that many more people have been infected than is commonly believed and that the disease is harmless for most. A sample of 10,000 is nice and big to show prevalence in a population like MLB employees that looks more like the general public than a sample of pregnant women or homeless persons does. We’ll have our best sense yet soon of how many average Americans have contracted the illness. I’m curious to see what sort of regional effects there are, too. We can expect a higher rate of infection among New Yorkers right now than among Kansans, obviously, but how much higher? Regional disparities in immunity are going to complicate interstate travel over the next 18 months, and the wider those disparities are, the more complicated it’s going to be.

Exit question: If the infection rate is 36 percent in a homeless shelter, what is it among the medical staff at a New York hospital right now? According to the CDC, health-care workers make up 10-20 percent of the entire country’s positive cases. If there really is a gigantic share of asymptomatic carriers in any discrete group, it may be that a huge percentage of health-care pros already have had it.