The novel coronavirus, true to its name, continues to display properties that are surprising once discovered. The official data from the Centers for Disease Control and Prevention on reported cases and deaths appeared to indicate that it is much more lethal than other viral infections (like the flu). In Pennsylvania we have had about 1,600 deaths out of 40,000 cases, or a death rate of 4% (slightly less than the overall national rate but above that in rural states).

However, new research using antibody tests that detect whether the test taker had an infection have consistently shown much higher rates of prevalence than indicated by identified cases. In New York the proportion showing positive antibodies was 14%, nearly 10 times the measured fraction with infections. Closer to home, a study of women who delivered in the University of Pennsylvania Health System found a rate of 8%, again much higher than the identified cases.

The antibody test itself, like almost everything else in the epidemic, is not all that accurate. Epidemiologist Michael Osterholm from the University of Minnesota appearing recently on Meet the Press argued that the rate of false positives (your test indicates disease you really didn’t have) is at least 50% —though the Penn testing is more accurate than this. Nevertheless, the main conclusion from this work seems clear—there are many more people who had coronavirus than had reported cases.

Television commentators on the epidemic, familiar with arithmetic, quickly made the obvious calculation—if you divide the number of deaths by a much larger number, the death rate will fall a lot, probably below 1%, and potentially in the range of the flu or other pandemics. This discovery was presented as much-sought-after good news.

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But is it? Probably not, and here is why. Think about two sets of people who truly have had coronavirus. Some were detected or reported, and the numbers across the US are accurate for them. Less certain but surely large is the number of unreported cases, people who either got better or died without knowing they had the virus. We do not know the number of deaths in this group from the virus—there must have been some but they would have been attributed to other causes, and are probably at a much lower rate per person with undiagnosed disease than the rate among those with diagnosed disease. The important conclusion is that there were all the deaths from coronavirus that we already knew about plus some number that we are just now discovering—and more deaths are surely worse for the country than fewer.

We want to know the true death rate both to plan public health and economic stimulus measures, and to forecast for ourselves how likely we are to die if we have not been diagnosed yet but are seeking to break out of home confinement. However, this new information tells us that there are more deaths, and a higher death rate among all Americans, diagnosed or not. More people have died from coronavirus than we thought, even if you do not yet have a diagnosis you could still die from it. Things are worse, and also more complicated.

There are some useful messages from the bad news. The existence of undiagnosed disease increases the benefit from efforts to diagnose it (especially if the disease is just as bad if you catch it from someone who showed no symptoms). People who feel super-healthy should not mix with others either because they might be carriers or they might die without knowing why. The most positive implication is that those with antibodies may be protected if they go back to the community—but how much protection they have and for how long is still very much up in the air.

Finally, there is the ultimate “bad news-good news” story—if about 60% of people end up being infected (at least 40% more than have been infected so far), we will have herd immunity and the virus may die out for lack of victims. Still, the fact that the “invisible enemy” is even more invisible than we had thought is a strong argument for continued caution.

Mark V. Pauly is Bendheim Professor in the department of health care management, professor of health-care management, and professor of business economics and public policy at the Wharton School, and professor of economics in the School of Arts and Sciences at the University of Pennsylvania. He is also a member of the Inquirer’s Health Advisory Panel.