I should clarify the headline. Antibody testing found 7.3 percent infected in Stockholm *as of mid-April.* We’re now six weeks removed from that, which explains why the country’s chief epidemiologist is estimating that more like 20 percent of the city’s population has now been exposed.

Is that estimate sound, though?

The disease spreads exponentially so six weeks really could be enough to have it more than double across the population. But exponential growth assumes people are carrying on business as usual, taking no precautions to limit infection. That’s not what the Swedes are doing. They’re practicing voluntary social distancing, limiting large gatherings, and mandating distance-learning for older students. Elementary schools and businesses are open, but naturally you’re not required to visit bars and restaurants and risk infection.

I don’t entirely follow the reasoning here:

Just 7.3% of Stockholm’s inhabitants had developed Covid-19 antibodies by the end of April, according to a study, raising concerns that the country’s light-touch approach to the coronavirus may not be building up broad immunity…

Sweden’s state epidemiologist, Anders Tegnell, said the Stockholm antibodies figure was “a bit lower than we’d thought”, but added that it reflected the situation some weeks ago and he believed that by now “a little more than 20%” of the capital’s population had probably contracted the virus.

However, the public health agency had previously said it expected about 25% to have been infected by 1 May and Tom Britton, a maths professor who helped develop its forecasting model, said the figure from the study was surprising.

“It means either the calculations made by the agency and myself are quite wrong, which is possible, but if that’s the case it’s surprising they are so wrong,” he told the newspaper Dagens Nyheter. “Or more people have been infected than developed antibodies.”

Tegnell clarified that the antibody results reflect prevalence in Stockholm as of mid-April, not the end of April, since it takes a couple of weeks to produce antibodies after you’re infected. Anyone infected after mid-April wouldn’t have been positive yet when the antibody tests were conducted in late April, in other words. So if I have the timeline correct:

1. Originally they projected 25 percent to have been infected by the end of April
2. Antibody tests as of mid-April showed only 7.3 percent infected
3. Tegnell estimates that 20+ percent are infected now, three weeks into May

That seems like a bad miss in modeling, as Britton acknowledges. But it’s in line with antibody testing all over Europe, which has consistently found lower-than-expected prevalence in hard-hit countries. Recall that recent antibody testing in Spain showed infections there were far fewer than modelers had projected early on in the epidemic, when the country was overwhelmed with COVID cases.

*If* Tegnell’s right that prevalence has jumped from 7.3 percent to 20+ percent in six weeks, though, then the logic of exponential growth suggests that the country (or at least Stockholm) is still on track towards herd immunity. But that’s not how other Swedish epidemiologists are interpreting the new antibody results:

Bjorn Olsen, Professor of Infectious Medicine at Uppsala University, is among dozen academics who have criticised Sweden’s pandemic response and labelled herd immunity a “dangerous and unrealistic” approach to dealing with COVID-19.

“I think herd immunity is a long way off, if we ever reach it,” he told Reuters after the release of the antibody findings.

Why is it a long way off if Tegnell’s model of exponential growth is correct, though? Is Olsen suggesting that maybe prevalence in Stockholm *hasn’t* grown very much beyond 7.3 percent in mid-April? I ask because the Sweden news reminded me of how flat New York City’s rate of prevalence was across three rounds of antibody testing in April and May, from 21.2 percent in round one to 24.7 percent in round two to 19.9 percent in round three. Granted, there’s a meaningful difference between NYC and Stockholm: New York is locked down and Stockholm isn’t, so we’d expect prevalence to increase more quickly in Stockholm lately. But again, the Swedes are social-distancing voluntarily to limit the spread.

So how do we square Tegnell’s and Olsen’s assessments? Is Tegnell overestimating how many people in Stockholm have been infected by now, in which case herd immunity might still be far away, or is Olsen underestimating it, in which case it might not be? The answer matters a lot in plotting a viable strategy, as Sweden had the highest per-capita death toll in all of Europe over the past week. If that’s as bad as things get before herd immunity starts to set it, maybe it’s a price worth paying. If instead Sweden has many months of that to come, hoo boy. There’s progress on other fronts lately, though, per Reuters: “The number of COVID-19 patients in intensive care in Sweden has fallen by a third from the peak in late April and health authorities say the outbreak is slowing.” Is that an early sign of herd immunity or a byproduct of increased social distancing — or, maybe, just weather effects from spring turning towards summer?

One last thing I don’t understand about Sweden. Why aren’t they testing more? Reuters notes that tests are reserved mainly for hospitalized patients and health-care workers, and that capacity is currently running at less than a third of the 100,000 per week the government’s aiming at. Sweden is currently 58th worldwide in tests per capita, at a rate less than half of the U.S. Even if you’re taking a laissez faire approach to managing the epidemic, as the Swedish government is, logically you should want to be able to detect small outbreaks as they get going so that you can intervene to protect vulnerable people (the elderly and infirm) who are at risk from them. But if the answer to that is “Why test if you’re striving for herd immunity?”, then why bother testing anyone at all? Why should Sweden have a goal of 100,000 tests per week? Just let the COVID chips fall as they may.

Speaking of testing in the U.S., here’s an ominous report from The Atlantic that’s worth flagging. The good news is that testing here has increased dramatically over the past month. The bad news is that the powers that be may be conflating two very different types of tests:

The Centers for Disease Control and Prevention is conflating the results of two different types of coronavirus tests, distorting several important metrics and providing the country with an inaccurate picture of the state of the pandemic. We’ve learned that the CDC is making, at best, a debilitating mistake: combining test results that diagnose current coronavirus infections with test results that measure whether someone has ever had the virus. The upshot is that the government’s disease-fighting agency is overstating the country’s ability to test people who are sick with COVID-19. The agency confirmed to The Atlantic on Wednesday that it is mixing the results of viral and antibody tests, even though the two tests reveal different information and are used for different reasons.

Several states—including Pennsylvania, the site of one of the country’s largest outbreaks, as well as Texas, Georgia, and Vermont—are blending the data in the same way…

“You’ve got to be kidding me,” Ashish Jha, the K. T. Li Professor of Global Health at Harvard and the director of the Harvard Global Health Institute, told us when we described what the CDC was doing. “How could the CDC make that mistake? This is a mess.”

In other words, the CDC’s numbers reflect both PCR tests (the nose/throat swab that confirms if you’re infected now) and antibody tests (blood tests that confirm if you’ve been infected previously and recovered). There’s no way to tell how many people are actively infected when you blend the numbers that way, and thus no way to tell whether the outbreak is currently growing or shrinking. It’s suspicious that some states are doing it as well since folding the number of antibody tests into the number of PCR tests smells like a quick and easy way for a state to artificially boost its testing numbers in response to criticism that it’s not testing enough. This could also help explain why the positivity rate in the U.S. has dropped so dramatically lately. We (or at least some states) may not be testing many more people for active infections. We may just be inflating the total number of daily tests with an inapposite form of testing.

Exit question: When exactly did the CDC become such a garbage agency?