The percentage of people who die after testing positive for the coronavirus is rising even as thousands of new U.S. cases are identified each day, a troubling preview of the weeks and months that lie ahead.

Epidemiologists and experts say increased case fatality rates are a natural function of a deadly virus running its course: The people who succumb today were probably infected as long as a month ago, when the number of cases began accelerating.

"As the epidemic picks up and you see a sudden rise [in cases], deaths will be very low," said Michael Osterholm, director of the Center for Infectious Disease Research and Prevention at the University of Minnesota. "It's just new onsets. And then as they work through the process, becoming severely ill, becoming hospitalized, being in the ICU and then dying, it's a long-term process of three or up to four weeks."

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That long-term process is starting to show itself in states that were at the heart of the second wave of the outbreak in the U.S.

In Connecticut, where commuter communities outside New York City have been hit hard, the case fatality rate has risen 3 percentage points in just two weeks. Today, 7.6 percent of all confirmed COVID-19 patients have died, among the highest rates in the nation. That equates to 1,431 deaths over just the last two weeks.

In Massachusetts, Louisiana and Minnesota, case fatality rates are up 2 points, to 5.3 percent, 6.2 percent and 7.5 percent, respectively.

Massachusetts has been hit particularly hard. Nearly 30,000 Bay State residents have tested positive in just the past two weeks, and 2,143 have died.

Other states where fatality rates are on the rise include large states with significant outbreaks such as California and Illinois and smaller states that have seen fewer cases such as Maine, Vermont and West Virginia.

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The overall mortality rate among those who contract the coronavirus is unknown because so many people can be asymptomatic and might never be tested. Antibody tests conducted in some U.S. cities suggest that hundreds of thousands of people, and perhaps as many as a million in New York City, have been infected — far greater than the number of people who have tested positive.

The World Health Organization estimated last month that the coronavirus and the COVID-19 disease it causes would carry a mortality rate below 3.4 percent — and likely far below that. More recent estimates have ranged from 0.2 percent, or about twice as bad as an influenza pandemic, to 0.5 percent.

But the rising rates across the country suggest the death toll is likely to increase, even as states begin to loosen restrictions on business operations and social gatherings. After those restrictions are loosened, people who have already contracted the virus will continue to get sick, and some will die. The number of deaths is not likely to decline until three or four weeks after the number of cases diagnosed on a daily basis begins dropping significantly.

"What you're seeing in deaths is transmission that occurred three to five weeks ago, and it's just now catching up. You can flatten the curve with infections and still see deaths going up," Osterholm said.

Case fatality rates vary widely across the country, which is in part a function of each state's capacity to conduct testing. The greater the capacity, the more low-symptom and asymptomatic cases will be identified — and, therefore, the lower the mortality rate. In states with less capacity, only the sickest, and therefore those most vulnerable to the worst outcomes, will be tested.

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A low case fatality rate is not necessarily a positive sign for the long run, though. South Dakota is one example of fatalities as a lagging indicator.

Two weeks ago, the state had confirmed only 730 cases. Today, that figure is more than three times higher, at 2,213 cases. But only 11 residents have died, a case fatality rate of about 0.5 percent. In the next several weeks, those who have been diagnosed more recently will either recover or slide in the other direction.

Prabhjot Singh, a physician and health systems expert at Mount Sinai and the Icahn School of Medicine in New York City, said states with higher rates are experiencing what he called the "streetlight effect." The coronavirus is transmitting within communities across the country, but health systems are only identifying patients who have been pushed into what might be considered the halo of a streetlight when they become sick enough to require care.

Other countries have seen their case fatality rates fall, and transmission of the coronavirus virtually grind to a halt, through a testing regime that is far more robust than any that have been attempted in the United States. An Australian study of a surveillance system that screens for fever and cough and rapid identification of new cases could effectively eliminate community transmission.

Several states and cities have launched early programs that aim to bolster their surveillance and testing regimes. Massachusetts has joined with the Boston-based nonprofit Partners in Health to deploy an army of contact tracers. New York, New Jersey and Connecticut are working to set up a joint program.

Other states such as Kentucky and Minnesota have ramped up testing, to the extent that any resident who wants a test can get one, regardless of symptoms. Residents in Kansas City can now sign up for tests even if they haven’t shown symptoms.

But the United States remains a long way from building the capacity needed to duplicate successes seen in countries such as Australia, New Zealand, Taiwan, Singapore and South Korea. A new analysis by Harvard researchers for the news publication Stat found that more than half of U.S. states still lack the testing capacity necessary to bring the virus under control.