The Martha’s Vineyard Hospital reported its 40th positive Covid-19 test on Thursday, as case numbers continue to steadily climb on the Island during the first week of August.

The new case reported Thursday — a female in her 50s — is the third case reported by the hospital this past week and the fourth overall. There are now six active coronavirus cases on the Island, according to the most recent demographic report from the Island boards of health.

The Island’s total coronavirus caseload now sits at 76, with 56 patients receiving a positive PCR (laboratory) test, 17 testing positive for viral antibodies and three diagnosed symptomatically with the virus.

The hospital continues to test symptomatic patients and their close contacts for the virus. TestMV — a comprehensive testing site at the regional high school — is focused on testing asymptomatic patients for the virus.

One case was reported Tuesday by TestMV.

Meanwhile, Quest Diagnostics announced mid-week that innovations at its laboratories nationwide will enable faster turnaround times for test results, including at the TestMV site. The innovations in test pooling and RNA extraction have cut wait times for results from seven to around five days, according to a press release, and could be available in as quickly as three days by early next week.

The new cases this week came as daily case numbers throughout the state have inched up and down. Tuesday marked the first day since June when daily case numbers exceeded 400 in the commonwealth. Case counts are also on the increase on Nantucket and Cape Cod.

A new out-of-state travel order issued by Gov. Charlie Baker took effect August 1, requiring all travelers from outside New England, New York and New Jersey to fill out an online travel form and quarantine for 14 days, or show proof of a negative test from the past 72 hours. On Wednesday Rhode Island was removed from the “exempt” list due to a recent rise in cases in the Ocean State.

The TestMV site is operated through a unique public-private partnership among the Island boards of health, Quest Diagnostics and Island Health Care. Tests are sent for processing to a Quest laboratory in Marlboro.

Late last month TestMV announced that results would be delayed due to a national backlog and surge in testing demand. Previously results were available in 24 to 48 hours.

But in the announcement Wednesday, Quest said a variety of scientific developments and a plateau in testing demand had allowed it to cut expected wait times at its labs nationally.

“We have recently increased capacity through several lab innovations,” the announcement said. “These include the use of specimen pooling, which is now in place at three of our laboratories, and improvements in RNA specimen extraction. We have also expanded our lab referral network to include a half dozen laboratories to facilitate greater access to Covid-19 molecular diagnostic testing.”

Specimen pooling allows testing sites to compile individual Covid-19 tests into one batch, or pool, and then evaluate all the tests at once. If the test comes back negative, then all the samples are negative. If the test comes back positive, then all are re-tested individually, making the testing process more efficient and cutting wait times.

The technique, combined with speedier ways to extract specimen RNA, is a more efficient way to evaluate patients in regions or populations with low incidences of the disease, according to Quest. Pooling is being done at the laboratory’s Marlboro facility.

Island Health Care posted a notice on its website Wednesday announcing the shorter turnaround times.

“For all patients, the average turnaround time is five days and is expected to be three days by next week,” it said in part. “For our priority one patients, the average turnaround time is two days and is expected to be one day by the end of this week or early next week.”

TestMV has now tested nearly 8,000 people on the Island for the virus.

In its daily online update Thursday, the hospital reported that it had tested 3,166 patients for the virus since mid-March, with 40 residents testing positive, 3,087 testing negative and 39 tests still pending.

A board of health update later in the day reported that TestMV has tested 7,818 patients for the virus since opening in late May, with 16 tests coming back positive, 7,035 testing negative and 767 tests still pending.

The new case on Thursday is the 15th person between age 50 and 60 to test positive for the virus — more than any other demographic age group. The age breakdown for positive test patients is as follows: eight under the age of 20; 13 in their 20s; six in their 30s; three in their 40s; 15 in their 50s; eight in their 60s; and three over the age of 70.

Statewide, the DPH reported 162 new cases on Thursday — down from numbers that reached in the 400s earlier in the week. More than 111,000 residents have tested positive for the virus throughout the state.

The state also reported 32 new deaths on Thursday, bringing the total to 8,470. No deaths have been reported on Martha’s Vineyard.