Scientific experts on the White House’s coronavirus task force have offered the same warning over and over: The number of confirmed cases of coronavirus will continue to increase over the short term because of a backlog in testing.

“There were individuals who had been tested who hadn’t had their specimen run because of the slow throughput,” Deborah Birx said Wednesday. “So we will see the number of people diagnosed dramatically increase over the next four to five days. … To every American out there, it will be five to six days worth of tests being run in 24 to 48 hours.”

In other words, as Anthony S. Fauci said Tuesday, the efforts to contain the virus, including closing major events and other social-distancing efforts, may seem like they aren’t working even though they are. Or may be.

“You could see the virus going up and up, and your effect, your work — what you’re trying to do — may actually be having an effect, but you may not see it because it’ll still be going up,” Fauci, director of the National Institute of Allergy and Infectious Diseases, said. “And as you’re trying to implement your interference with the virus, you may not realize that you are actually interfering.”

Those points are well taken in the context of the government’s efforts. But it also serves as a reminder that we don’t actually know the number of infections in the United States — and we may not for some time to come.

The pattern in the confirmed cases is clear: Growth has been exponential. Two weeks ago, there were 221 confirmed cases. One week ago, the total was 1,697. Now, the number is more than 11,000.

That growth is a function of thousands of new cases being confirmed each day. On Monday, fewer than 1,000 new cases were confirmed. On Tuesday, nearly 2,000 were. On Wednesday, it was nearly 3,000.

As Birx said, that is in part due to the increase in the number of tests being completed. In the past week, the number of tests that have been completed has similarly begun to increase more quickly. (Test totals for more recent days are incomplete.)

Since the end of February, state public health labs have increasingly been conducting coronavirus tests, adding the vast majority of the tests that have been completed since then.

This raises a critical question, though: To what extent is the increase in the number of cases a function of the increase in the number of tests being completed?

Since the beginning of the month, as the number of tests and the number of confirmed cases have both risen, the number of tests completed for each positive result has fallen. On March 6, for example, there were 1,764 tests received by the CDC and 98 confirmed cases — about 18 tests for each confirmation that day. (We’ll note that it’s not clear that the daily confirmation numbers necessarily derive from the tests received the same day.) By March 13, there were 4,687 tests and 550 confirmations, about 8.5 tests per confirmation.

Why? In part it may be because of where the testing is centralized; Birx said Thursday that testing was being prioritized in California, New York and Washington, the states with the most cases.

But in part it’s because the rate of confirmations is increasing faster than the rate of testing. In the period of March 6 to March 13, the average daily percentage increase in the number of confirmed cases was nearly twice the daily percentage increase in the number of tests completed.

Remember that these confirmations don’t entirely track with the actual spread of the illness. The CDC compiles data on the date when patients first noticed their symptoms, finding a slow increase each day in the number of patients first becoming noticeably ill. (Here, too, given the variable onset of symptoms, more recent data probably is incomplete.)

If we compare that with the number of new cases added each day, we see the lag time that Fauci mentioned earlier this week. While we can’t determine specifically when particular cases first started manifesting symptoms, we can see that there is a period of five or more days between the increase in symptoms and the increase in confirmations.

Part of that gap depends on the testing itself, which reportedly can take multiple days.

These figures, though, make clear the uncertainty about the top-line number of confirmed cases. That number, those 11,000-plus confirmed cases, depends on the number of tests being conducted. It also trails the actual onset of symptoms — which itself trails infection by days or weeks. One expert estimates that there may be between 50,000 and 500,000 cases in the United States.

It’s important to note, too, that President Trump himself has repeatedly expressed a desire to see that 11,000-plus figure remain as low as possible. He’s said so publicly and has privately pressured his administration to keep the figure low, according to reporting. He’s done so even while criticizing the Obama administration for its handling of the H1N1 outbreak in 2009, using after-the-fact estimates of its spread and not the numbers that were reported as that outbreak expanded.

Even without any pressure from the top, the number of coronavirus cases as reported is demonstrably low and will continue to grow. That doesn’t necessarily mean efforts to control the virus aren’t working. It does, however, mean that efforts to contain it in the first place didn’t.