Harvard’s law school has placed one of several coronavirus self-test dropoff boxes in its Caspersen Student Center. (Photo: Marc Levy)

The city has performed approximately 11,000 free Covid-19 tests for residents since the spring, more than half in July and August alone, the city manager and Cambridge public health chief told city councillors Monday. Still, that number is dwarfed by the total number of coronavirus tests received by Cambridge residents from all test providers as of Wednesday: 90,707, according to the state Department of Public Health.

As college students have returned to the city and many undergo repeated tests to stay on campus, the numbers have swelled. A weekly state health department report says 25,496 tests of residents were performed in just the two weeks that ended Wednesday. The state agency has said it considers college students residents of the community where they attend school unless the department has different information, although it does not break out the numbers ascribed to students.

Despite these prodigious numbers, the demand for testing has continued. Appointment slots for city tests have filled up quickly. As of Wednesday there were none left this week, according to a daily city update. The city is accepting requests for appointments week by week.

The number of tests is certainly higher than the number of individuals getting them – students at Harvard University and the Massachusetts Institute of Technology, for example, may be tested as many as three times a week. And some people have received multiple free tests from the city.

Neither the city nor the state health departments has reported a figure for the number of individual Cambridge residents who have been tested, though the state does post the total statewide. A graph on the state health department’s daily Covid-19 dashboard indicates that this month, more repeat tests than initial tests were being performed on most days.

Susan Feinberg, spokeswoman for the Cambridge Public Health Department, was asked Tuesday whether the department could provide the number of individuals tested in the city program. This story will be updated if she responds.

The state Department of Public Health also reports the percentage of positive tests as well as the percentage of individuals who test positive; the rate for individuals is higher. For example, on Wednesday almost 2 percent of individuals tested positive while a little less than 1 percent of tests were positive.

The city’s average positivity rate of 0.16 percent over the last two weeks appears to apply to tests, not individuals.

The city is paying $20 to $25 per test “currently”  to the Broad Institute of Harvard University and MIT, which is analyzing nasal samples from the city program at its high-speed viral testing laboratory, spokesman Lee Gianetti said Sunday.  “This covers the cost of test kits, lab processing and administration,” he said. Gianetti said Cambridge received $250,000 from MIT and is contributing another $150,000 of its own funds for a total allocation of $400,000 for free Covid-19 tests. The city’s public health department oversees the program. Gianetti didn’t answer a question about whether the city receives reimbursement from insurers for tests. Residents are not asked for a Social Security number or insurance information when they sign up for a test at an online appointment site.

Broad also performs tests for more than 100 colleges and universities, including the two with which it’s affiliated. And it tests nursing home residents and residents of “hot spot” cities with high infection rates for the state.

A press release from the Broad Institute from Sept. 2 said the lab is charging the schools $25 a test and has a standard fee of $35 to $50 per test. The institute drops its charge to $25 for customers that have a “critical public need or that have a high and sustained volume,” the press release said.

Private laboratories charge as much as $150 a test, the institute said.