The COVID-19 outbreak that has infected more than half a million Americans is killing people or causing them to become seriously ill at vastly different rates in different states, baffling scientists who are still learning about the coronavirus that causes the illness.

The virus so far has killed at least 23,529 people in the United States, a case fatality rate of just over 4 percent.

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But the true mortality rate of COVID-19 is almost certainly much lower. Studies have showed that many infected with the virus show no symptoms, or nothing worse than a common cold, suggesting that the actual number of people who have contracted the virus is much larger than the 579,390 who had tested positive as of Tuesday morning.

The worst outcomes have come in states with the highest number of cases. Experts said that is likely a function of state rules that govern who is eligible to get one of the limited number of tests available: Only those who are sickest, and thus most likely to die from the disease, are tested, while those who are likely to make a speedy recovery are sent home to convalesce.

“In lots of places that are hard hit, what they have to do is limit testing to those who have symptoms, and sometimes pretty severe symptoms,” said Amira Roess, an epidemiologist and global health expert at George Mason University’s College of Health and Human Services.

“Different states are having to make testing decisions. They're having to change their testing policies as they move through the epidemic.”

In Michigan, where 25,635 people have tested positive, the case fatality rate stands at 6.3 percent, the highest level in the country. New York, the epicenter of the outbreak in the United States, has recorded 10,056 deaths out of 195,031 cases, a fatality rate of 5.1 percent. And in Washington, where an early outbreak claimed dozens of lives at a nursing home, the case fatality rate stands at 5 percent.

Connecticut and New Jersey also have high case fatality rates amid outbreaks that are concentrated in the New York City suburbs.

Other states near the top of the list have large numbers of residents who suffer from the underlying conditions that seem to exacerbate the coronavirus. Kentucky, Oklahoma and Indiana all have relatively high case fatality rates, even though their number of confirmed cases is lower than in other states; they are among the states with higher-than-average obesity, diabetes and smoking rates.

“If you're having a large number of elderly or people with underlying conditions getting infected, then you're going to have a higher case fatality rate,” Roess said.

On the other end of the spectrum are smaller rural states that have seen relatively few cases so far, and where geography or population density have created a sort of built-in social distancing.

Wyoming on Monday became the last state in the union to report a death from the coronavirus. It has only reported 275 confirmed cases. Utah and South Dakota both have case fatality rates under 1 percent, though the number of cases in South Dakota has risen rapidly for such a small state in recent weeks.

West Virginia, Montana, Hawaii and Idaho all have case counts under 2 percent. So does North Carolina, a larger state but one with a substantial rural population.

The United States is trending better than the global average case fatality rate, according to data compiled by the European Centers for Disease Control. Worldwide, COVID-19 has killed a little more than 6 percent of confirmed cases. The rates are much higher in places like Italy and Spain, where health systems were overwhelmed by a huge explosion of cases in early March and where fatality rates stand north of 10 percent.

But the United States is faring worse than places like Germany and South Korea, where aggressive testing regimes have identified more people with the coronavirus — and therefore, more people who show few if any symptoms and are most likely to recover. The case fatality rate in Germany is about 2.4 percent, while it stands at just 2.1 percent in South Korea.

In Iceland, where huge teams of contact tracers have fanned out across Reykjavik and the country's rural communities in what may be the world's most ambitious testing regime, the case fatality rate stands at 0.5 percentage points.

Case fatality rates in countries like China and Iran are unclear, as scientists raise questions about the accuracy and transparency of the data those nations have made public.

Epidemiologists say they will earn a better understanding of the true toll of COVID-19 once they are able to do broader studies, randomized tests — like a public opinion poll, but with blood samples — to see just how many people in society at large have been infected by the virus, including the asymptomatic cases who might never know anything is wrong with them.

“We don't have infection rates. We haven't done a very simple test in epidemiology, which is to try to randomly sample a population in an overall area,” said Jennifer Prah Ruger, director of the Health Equity and Policy Lab at the University of Pennsylvania. “We don't know how many people have been infected, have already recovered.”

Case fatality rates can change over time, and experts said they are already seeing a difference in states that promoted or enforced social distancing policies early on. The fast start to the outbreak in Washington state meant the fatality rate there was among the highest in the world in its earliest days — at one point in early March, nearly a third of the confirmed COVID-19 patients had died.

But as the state enforced distancing rules, and as the virus spread outside of the nursing home at its epicenter, the case fatality rate has dropped steadily. California, too, acted aggressively to ban large gatherings and encourage people to work from home, efforts that have paid off.

“The early social distancing has had a huge effect on mortality, which is what we're really trying to do. We may be closer to being able to come out of shelter in place than other locations,” said George Rutherford, an epidemiologist at the University of California-San Francisco.

In states that waited longer to implement strict measures, the fatality rate may be on the rise — and the number of cases is growing quickly. Southern states like Florida, Alabama and Georgia have seen their case counts rising in recent days, after governors in those states were slow to take steps like closing beaches, restaurants and bars.

“They've come to the party late in terms of social distancing, and there may still be a price to be paid,” Rutherford said.