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Over the past few days, some glimmers of relative hope have flickered down the end of what had seemed until recently a possibly endless tunnel. The COVID-19 news since the weekend isn’t all good; in a pandemic it rarely is, and yesterday marked the highest number of new deaths in the United States reported yet: 1,941, almost 50 percent higher than the previous peak, which came just on Saturday. In New York, the epicenter, 800 patients died yesterday of COVID-19, twice as many as on any day before, and now, in addition to those deaths registered by hospitals, 200 New Yorkers are dying at home each day, uncounted in the official statistics, perhaps ten times as many as died during a typical day before the pandemic arrived.

But also over the past few days, the number of new hospitalizations in New York has probably begun to flatten. San Francisco has started to think about what follows shelter in place. And, in perhaps the most significant development, revisions to the pandemic model developed by the Institute for Health Metrics and Evaluation (IHME) at the University of Washington suggested that the country would ultimately need fewer beds, fewer ICU beds, fewer ventilators and doctors and nurses and PPE — in short, fewer hospital resources of all kinds than was expected. More strikingly, it revised its most recent estimates for the ultimate coronavirus death toll downward by 11,765, or roughly 15 percent: from 93,531 to 81,766. A couple of days later, it revised them even more dramatically, from 81,766 to 60,415, or roughly 25 percent more.

These revisions may be eye-opening, in addition to being encouraging, because as recently as a week or two ago, the projections discussed by most public-health officials were much, much higher. When Donald Trump unveiled his “flatten the curve” chart, months after public-health experts began advocating that approach to the disease, he was working off the IMHE model, and suggesting that between 100,000 and 240,000 Americans would die. A model developed by the CDC projected a range between 200,000 and 1.7 million. The Imperial College model famously predicted 2.2 million deaths in the U.S. in a do-nothing scenario, and more than 1 million even if quite aggressive mitigation measures were adopted. As of April 2, a survey of public-health officials summarized by FiveThirtyEight found a median projection of around 263,000 deaths. The new IHME model suggests an ultimate toll less than one-quarter that number, about one-20th the figure projected in the Imperial College’s “mitigation” scenario, and less than one-30th what was projected in their “do nothing” scenario.

As Zeynep Tufekci has brilliantly written for the Atlantic, models like these are not meant to be crystal balls, producing projections we can all take to the bank, but a survey of possible futures that depend on what choices are made and what policies are engineered and implemented in response to the pandemic threat. Nevertheless, the gap between what experts projected a few weeks ago and what they are projecting now is absolutely astounding, and it is primarily a reflection of just how much has been done, and how quickly, to defend against and respond to the coronavirus. In many cases, we have achieved so much more than modelers even imagined possible that the range of outcomes we are now looking at did not even appear at the very low end of initial forecasts. The models weren’t “wrong,” exactly, they seemingly just underestimated how widespread, thorough, and steadily maintained social-distancing measures could be. How could they not? It can be easy to forget, a few weeks into something like a hemisphere-wide lockdown, just how absolutely unprecedented this public-health mobilization truly is: nearly every American in every state embracing punishing, restrictive quarantine-like isolation for the sake of the country as a whole. We are doing so willingly, with hardly any meaningful resistance to shelter-in-place guidance, even though the statistical profile of the disease, while brutal, would allow most Americans to think it was a much more significant threat to others (the case fatality rate here now estimated between 2 and 3 percent). This is solidarity I simply didn’t believe was possible in this country anymore and under any circumstances, and it has arrived in the space of just weeks, in the midst of national political chaos with tribal partisanship still boiling at a feverish peak. It is breathtaking.

The phenomenon is bigger than the U.S., of course, as are most aspects of this disease; as horrifying as Americans may find the lack of leadership in Washington, the U.S. response falls roughly in the middle of a range of governmental incompetence exhibited by the nations of Western Europe. But while governments in those countries were much slower than they could have been, they also moved quickly and in unison when they did — bringing them into line with aggressive actions taken by Asian countries to produce an unprecedented global response to the kind of collective-action problem we used to assume was almost unsolvable at the international level. The terrifying projections of economic impacts are, of course, a sign of how much the world as a whole has elected to cut back, as are the hard-to-believe recoveries of environments that were, until quite recently, toxically polluted. In Los Angeles, thanks to reduced car traffic, the air quality is now “best in the world,” and in Delhi, the air-quality index has fallen from 999 (the very top of the scale, and about three times the dangerous level of pollution) to 45 (which counts as almost unthinkably pristine). To cite just one additional figure, estimates now suggest more than 1.5 billion schoolchildren have already been taken out of school to protect against COVID-19. These interruptions may prove problematic in ways sociologists will study decades from now, since even beyond the possible traumas of a pandemic, childhood breaks in school tend to exacerbate educational inequities. And it may be the case that this collective, coordinated global bunkering is as much, or more, a reflection of personal fear and pandemic anxiety that it is of a truly universal and humanitarian sense of shared fate and collective purpose. Nevertheless, we have never seen anything like this globally, and in our lifetimes, we probably never will again. We need a plan for the next phase, urgently. But in the meantime, this moment of solidarity is truly something to behold.

How long that solidarity and those lockdowns continue is an open, and perhaps unanswerable question — none of us have been through this before, and it’s hard to predict at what point the commitment to collective safety might break, and break to what degree, opening up which share of the population to potentially lethal exposure. But how long our lockdowns last probably isn’t the most operative question when it comes to sorting out and planning for a medium-term COVID-19 future. Nor is it how many have died, how quickly those death rates are growing, or how long they have stayed flat. It also isn’t the number of hospitalizations, or confirmed cases, or total tests taken. All of these tell us about the state of the disease at various points in the recent past: cases reflecting infections one to two weeks ago, hospitalizations two to three weeks ago, and deaths three to four weeks ago. Of course, they also represent a baseline from which to project the future trajectory of that disease.

But in sketching that trajectory from that baseline, in forecasting the ultimate severity and shape of this pandemic, the most important data point is how many people are, or were, infected without anybody noticing. And our best hope, on that point, is that the disease is actually much more infectious than we’ve thought. That wouldn’t change how many are now sick or dying, but it would change, perhaps significantly, how many more we’d expect to fall sick, to require hospitalization, to require ventilators, and ultimately how many we’d expect to die.

Each of those deaths is a tragedy, and a horror. It is also a numerator, or part of one. The denominator is made up of how many people out there contracted the disease. And the fraction tells you, in theory, roughly how bad the outlook will be when the disease has finally passed through the entire population (which, barring the arrival of a vaccine, may take longer than the achieving of “herd immunity,” which is our clearest path back to “normal” life). The bigger that denominator, the less severe the disease at the population level: If roughly 13,000 Americans have died out of a total number of infected of 400,000 (the current “confirmed” case number), that is a pandemic nightmare of a certain scale; if 13,000 Americans have died out of a total number of infected of 4,000,000, that implies a final toll of a different, considerably lesser scale; and if the total number of infected is 40,000,000, even more so, with hospitalization and case fatality rates much, much lower as a result. It would also suggest that we are much further along the timeline of the pandemic and much closer to its conclusion. The bigger that denominator, the more people caught the coronavirus without realizing it, and the more people that caught the coronavirus without realizing it, the less severe the disease looks, and the faster we’ll likely get through its brutality and emerge into a strange-seeming post-pandemic future.

So, how big is that denominator number? Unfortunately, we don’t know. Worse, in the U.S., it is at this point, and for the very foreseeable future, unknowable. A second-order outrage about the pathetic, outrageous lack of test kits, and the backlog processing even the tests we do have, is that in addition to limiting our ability to treat those patients we know are ill and to take public-health measures to protect the vulnerable parts of our population, we have very little sense of the scale of the outbreak we are dealing with. When we can’t even test all those patients who show up at hospitals complaining of symptoms, we are miles from a clear sense of how many other people might be carrying the disease around — infecting others, of course, but also changing the size of that denominator. This is one of the reasons there has been so much recent enthusiasm for the possibility of what’s called serological testing, which can tell anyone, even the asymptomatic, if they’ve already acquired immunity. Until we do institute large-scale serological and “community testing” of that kind, we will be living in darkness.

Into that darkness have crept the amateur prognostications and “armchair epidemiology” of a loose confederation of contrarian writers, thinkers, and internet provocateurs I’ve started to think of as the “corona dark web.” Like the “intellectual dark web” before it, the corona dark web lives a bit to the right of the social-media commentariat generally (which is anchored somewhere on the center-left), is powered by a desire to prove conventional wisdom wrong, and is made up of almost entirely of men, mostly speaking outside of or beyond their areas of expertise. Perhaps the most notable avatar was Aaron Ginn, the Silicon Valley product manager whose Medium post “COVID-19: Evidence Over Hysteria” was a viral sensation on the right at the same time the president was downplaying the pandemic threat, and then was unpublished by Medium in an effort to remove disinformation from its site. (The post was later republished by RealClearPolitics and can be read here.) On its most respectable fringe, the corona dark web has included, at various points, Obama’s favorite legal scholar, Cass Sunstein; on its crazier fringe, libertarianism’s favorite legal scholar, Richard Epstein. It has also included Elon Musk and the head of the IMF, and Jair Bolsonaro, the president of Brazil, who despite his office falls clearly onto the crazy side of the ledger. And it surely includes Alex Berenson, a former New York Times reporter and the author of a recent controversial book asserting the mental-health risks of marijuana use are much higher than widely believed, who has become a sort of Twitter iconoclast — offering some amount of probably valuable perspective and skepticism, mixed with a kind of hysterical outrage that makes his analysis a bit harder to trust, especially for those who found their way to his contrarianism hoping for comforting news about the coronavirus (which, as Sean Trende has rightly pointed out, there seems to be a reluctance among credentialed, centrist social media to embrace any positive news). Berenson was recently praised by, among others, Brit Hume: “If you’re skeptical of the experts and suspicious of the computer modeling on Covid 19, the person to follow is former NY Timesman @AlexBerenson,” he wrote on Twitter. “He is doing the same sort of data analysis that the late Michael Crichton did on climate alarmism.”

The Crichton comparison is damning, and there are many good reasons to be skeptical about Berenson’s skepticism, too. But it remains the case that to a degree most Americans do not appreciate, there is an enormous amount we simply do not understand at this point about this disease. We do not know how lethal it is. We do not know the effect of seasonality and climate on its spread. We do not understand the age skew of health outcomes, since the disparities between elderly patients and young ones vary wildly country to country. We do not know, for sure, whether those who have survived it have long-lasting immunity, short-lasting immunity, or why, in a few cases, at least, survivors seem to have no antibodies to the disease at all. We do not know how to treat it, at least not very well, with some doctors suggesting in recent days that the conventional use of ventilators on end-stage COVID-19 patients may be ineffective at best, and possibly even damaging.

On all of these questions, and indeed many others, we are flying mostly blind. But, in the face of a pandemic, we probably need to stop ourselves from deciding to stop flying — as Amitha Kalaichandran argued as far back as February 26 in Scientific American, an argument echoed by Maggie Koerth April 6 in FiveThirtyEight and by Siobhan Roberts in her April 7 essay “Embrace the Uncertainty” in the New York Times. “At the end of the day,” Koerth wrote, “experts told me, when evidence is lacking, individuals and public health officials alike have to make a call based on what we do know, our personal experiences and our own understanding of risk and risk management” — meaning, in other words, “accepting that, sometimes, we’ll just have to do the best we can without a clear set of instructions.” That’s because, as the World Health Organization’s executive director of Health Emergencies, Michael Ryan, put it during a presentation about the global coronavirus response back on February 13, uncertainty can’t be an excuse for inaction. When it comes to pandemics, he said, “you must react quickly. You must interrupt the chains of transmission. Speed trumps perfection. The greatest error is not to move. Be fast and have no regrets.”

On many of these questions, the voices of the corona dark web are cultivating further uncertainty — which is to say, some mix of complacency and delay. The more irresponsible members are advocating worse — indifference to human suffering at a terrible scale. But embedded in the skeptical discourse is the highly important query about that total case-number denominator. On Stat News last month, the contrarian Stanford professor of epidemiology and public health, John P.A. Ioannidis, suggested that the quarantined Diamond Princess cruise ship represented the best contained, controlled environment in which to measure both infectiousness and fatality — and based on that data, infectiousness was higher and fatality lower than most conventional models suggest. More recently, the investor Bill Ackman, a few weeks ago a coronavirus “bear,” announced that he was growing more optimistic, even in the medium term, because he saw reason to believe “the asymptomatic infection rate could be as much as 50X higher than expected.”

To me, the most compelling of these analyses came from Christopher Balding, a business professor in Vietnam specializing in China — compelling in part because he refrained from offering concrete projections of his own, instead merely demonstrating that both small changes to our understanding of the disease’s infectiousness would amount to significant changes of our understanding of its severity, and that we had pretty good reason to believe that estimates of its infectiousness were, by and large, too low: namely, small-scale community-testing efforts that revealed higher-than-expected infection levels in the general population (and therefore a lower share of severe cases). An Economist analysis looked at the unusual spike of doctor visits arising from “flu-like symptoms” — atypical for this time of year — and suggested that COVID-19 may have spread as much as 200 times as fast as widely understood. This would amount to a total rewriting of our understanding of the disease; as the authors suggest, it would mean the disease was only about as lethal as the flu, though very much easier to catch.

Are these analyses hard-nosed assessments or a form of contrarian wishful thinking? It is too early to say for sure, but we are now beginning to get glimmers of an answer, and, though they are just glimmers, they are not uniformly encouraging. The WHO has long maintained that asymptomatic carriers of the disease represent about a quarter of all infected — which would suggest that, in a perfect and universal testing environment, we’d find a third more carriers of the disease than we’d find just by testing those presenting with symptoms. This would be a significant increase of the infected population, but not one that radically changes our picture of the severity of the disease. In Iceland, such a system as been instituted, and though only one percent of those tested were found positive, the number for asymptomatic carriers is higher: 50 percent of infected Icelanders don’t know they are carrying COVID-19. This is twice as high as the WHO figure, as so, by this logic, relatively good news. But even a doubling of the denominator does not change our picture of the disease that dramatically — it is not Bill Ackman’s 50X, in other words, let alone the Economist’s 200X. It is also in line with a new CDC “renanalysis” suggesting that the infectiousness of the disease might be twice as high as conventional wisdom recently held — a striking revision for those who remember the concern-trolling around those raising earlier alarms about elevated infectiousness rates, though not one that amounts to a basic reconceptualization of the nature of the disease or what we can expect from it. A new, small-sample serological survey in Germany holds more promising results: 14 percent of those tested carried coronavirus antibodies, meaning they’d already been exposed the disease, orders of magnitude more than is suggested by their confirmed case count of less than one-tenth of one percent of their population.

It is not easy to know how to interpret this range of findings — each reflecting different testing protocols and measuring the state of the disease in different populations. And of course, the broader lesson of pandemic modeling and its encounter with public health and public knowledge over the past few months is: Models and statistical analysis are surely helpful, indeed the best we can do when operating in a state of testing ignorance, but they are not as helpful as tests. Which is why we need much more testing — here in the U.S., but everywhere else as well. We are still, presumably, months away from a testing regimen here that could tell us the full scope of the disease. In the meantime, we should all be hoping that when those tests do begin to return results, they show more of us, not less, got sick. Indeed, we should be hoping that many more of us are sick right now.