As some governors consider easing social distancing restrictions, new estimates by researchers at Harvard University suggest that the United States cannot safely reopen unless it conducts more than three times the number of coronavirus tests it is currently administering over the next month. Average Daily Coronavirus Tests in the U.S. Level needed to safely reopen 152 tests 150 tests per 100,000 people (7-day average) 120 90 Current level 45 tests 60 30 March 4 April 15 May 15 150 tests per 100,000 people (7-day average) Level to reopen 152 tests 120 90 60 Current level 45 tests 30 March 4 April 15 May 15 An average of 146,000 people per day have been tested for the coronavirus nationally so far this month, according to the COVID Tracking Project, which on Friday reported 3.6 million total tests across the country. To reopen the United States by mid-May, the number of tests performed every day should be 500,000 to 700,000, according to the Harvard estimates, which is a daily minimum of about 152 tests per 100,000 people. That level of testing is necessary to identify the majority of people who are infected and isolate them from people who are healthy, according to the researchers. About 20 percent of those tested so far were positive for the virus, a rate that the researchers say is too high. “If you have a very high positive rate, it means that there are probably a good number of people out there who have the disease who you haven’t tested,” said Ashish Jha, the director of the Harvard Global Health Institute. “You want to drive the positive rate down, because the fundamental element of keeping our economy open is making sure you’re identifying as many infected people as possible and isolating them.” The researchers said that expanded testing could reduce the rate to 10 percent, which is the maximum rate recommended by the World Health Organization. In Germany, that number is 7 percent, and in South Korea, it is closer to 3 percent. There is variation in the rate of testing and positive results among states, but most need to administer more tests to get to the level the researchers suggest — a minimum of about 152 tests per 100,000 people each day.

Average Daily Coronavirus Tests Per 100,000 people Alabama Ala. 44 152 Alaska Alaska 31 Arizona Ariz. 21 Arkansas Ark. 35 California Calif. 26 Colorado Colo. 29 Connecticut Conn. 85 Delaware Del. 67 District of Columbia D.C. 66 Florida Fla. 47 Georgia Ga. 34 Hawaii Hawaii 47 Idaho Idaho 28 Illinois Ill. 47 Indiana Ind. 37 Iowa Iowa 27 Kansas Kan. 25 Kentucky Ky. 19 Louisiana La. 124 Maryland Md. 41 Massachusetts Mass. 92 Michigan Mich. 34 Minnesota Minn. 24 Mississippi Miss. 84 Missouri Mo. 35 Montana Mont. 29 Nebraska Neb. 28 Nevada Nev. 33 New Hampshire N.H. 32 New Jersey N.J. 70 New Mexico N.M. 72 New York N.Y. 118 North Carolina N.C. 34 North Dakota N.D. 52 Ohio Ohio 22 Oklahoma Okla. 57 Oregon Ore. 30 Pennsylvania Pa. 44 Puerto Rico P.R. 13 Rhode Island R.I. 185 South Carolina S.C. 28 South Dakota S.D. 50 Tennessee Tenn. 51 Texas Texas 27 Utah Utah 51 Vermont Vt. 76 Virginia Va. 23 Washington Wash. 34 West Virginia W.Va. 41 Wisconsin Wis. 25 Wyoming Wyo. 56 Notes: Testing levels shown are a 7-day moving average. Reporting methods and regularity can vary. Some fluctuations in the data can be because of a gap in reporting or a change in the reporting method. Maine was excluded because consistent and reliable data was not available.

In most states, people who had severe symptoms, worked in health facilities or were otherwise hospitalized were given priority for testing. The goal of the testing level recommended by the researchers would be to test nearly everyone who has mild or severe flulike symptoms, and an average of 10 contacts for each person who tests positive for the virus.

A shortage of test kits and technical flaws in the United States significantly delayed more widespread testing of the virus, letting it spread undetected for weeks. With more than 695,000 cases as of Friday, the country has the highest number of known cases in the world.

Health experts said that if the U.S. had tested earlier and more, the outbreak would have been better contained. Caitlin Rivers, an assistant professor at the Johns Hopkins Center for Health Security, said that since that did not happen and the virus spread rapidly, it has made sense to prioritize testing for those in hospitals in recent weeks.

“It does make sense, given constraints, to focus on people with severe illness, because you need that information to guide their care,” Dr. Rivers said.

In mid-May, however, when the researchers estimate infections will have subsided somewhat and states are looking to reopen their economies, Dr. Jha believes vastly expanded testing will be crucial.

“I want to be able to identify everybody who is even mildly symptomatic,” he said. “So when I wake up one morning and have a sore throat and a fever, I should be able to go get tested. And then I want to be able to test all of my contacts if I turn out to be positive, so that I can do the test, trace and isolate strategy that’s so critical to allowing us to open up and stay open.”

New Jersey currently has the highest positive rate among all states — about half of the 157,000 coronavirus tests that it has conducted so far have come back positive. That suggests that many of the people in the state who have the coronavirus have not been tested. And recently, testing in New Jersey has started to decline.

Average Daily Tests in New Jersey Level needed to safely reopen 152 tests 200 tests per 100,000 people (7-day average) Estimated actual cases 150 100 Current level 70 50 Identified cases 0 March 4 May 15 April 15 200 tests per 100,000 people (7-day average) Estimated actual cases Level to reopen 152 tests 150 100 Current level 70 50 Identified cases 0 March 4 May 15 April 15 Note: Estimated cases are five times the number of cases identified. The researchers estimate that at least 80 percent of people who have the virus have not been tested.

The state’s testing has been hindered by setbacks, including long lines at testing facilities and a shortage of health care workers and testing swabs.

Christopher Neuwirth, an assistant commissioner at New Jersey’s Health Department, said the state’s recent lag in testing could also indicate that fewer people are trying to get tested.

“In the days and weeks up until testing was available, there was a huge pent-up demand,” Mr. Neuwirth said. After that, he said, the public became more aware of the criteria for testing. “People really paid attention and really heard the messaging that you have to be symptomatic.”

That messaging will have to be reversed, Dr. Jha said, once testing is expanded.

“We need to switch from saying to people, ‘if you have mild symptoms, if you’re not feeling super sick, don’t come and stay at home,’ to ‘if you have any symptoms, you need to come in to get tested right away,’ ” he said.