The number of new coronavirus cases in Hawaii has increased slightly, nearly reaching half of all of May’s cases in the first week of this month. But Hawaii’s health director says the state continues to be positioned well in its response to the pandemic.

“We’re still in a very enviable position,” Bruce Anderson said Saturday by phone, adding that Hawaii continues to have the lowest number of cases in the country and the lowest number of deaths per capita from the coronavirus. “We’ve been able to maintain that status despite all the reopenings that are occurring.”

He said Hawaii is likely to see some increase in cases as the economy continues to reopen, but is currently not seeing widespread transmission in the community.

“This isn’t a situation where we want to get down to zero and expect to keep it there,” Anderson said. “We have to live with COVID-19 for years to come. I think we’re in a good place now, and hopefully we’ll stay there.”

On Saturday, the state Department of Health reported nine new cases in Hawaii, including eight on Oahu and one case involving a boy in Alaska who was included in the state count because he is a Hawaii resident. The state’s total number of cases stands at 673 and the death toll, which hasn’t changed in more than a month, remains at 17. Since June 1, there have been 22 cases reported in Hawaii, compared to 46 reported in May.

Of Saturday’s eight new cases, six came from the same household in Waipahu with one of them a coworker of a previous case. The two remaining cases were also household members of previous cases, highlighting the importance of contact tracing, Anderson said.

He said the new cases demonstrate the difficulty in preventing transmission of the disease within a household when someone in the household is infected.

He said the Health Department has been working with the Hawaii Public Housing Authority and agencies to knock on hundreds of doors in Kalihi, Palolo and Waipahu, where they provide educational outreach to low-income residents to prevent the spread of the virus. He said residents in those areas may be at higher risk of contracting the disease because they live in close proximity or have large numbers in their households.

“There’s an active effort in the Waipahu area now to identify possible cases, and also to provide outreach and education to those communities,” he said. “I think these cases were identified through that effort.”

Of the nine cases on Friday, three of them involved people who were suspected of being positive in March, but tests for them had initially come back negative. The state still had them isolate as a precaution and after retesting the samples found they actually were carriers.

Three of Friday’s cases involved employees working at long-term care facilities on Oahu — two at Kalakaua Gardens and one at Mauna­lani Nursing and Rehabilitation Center, which is a concern for the state because of outbreaks at nursing homes on the mainland and the vulnerable people in the facilities.

Anderson said the two cases at Kalakaua Gardens were not related to the other facility in East Honolulu, and some were kitchen workers; none was involved in direct patient care. He said both facilities had safety measures in place, such as physical distancing rules and universal masking. Staff and patients were also being tested at both facilities as a precaution.

“We don’t think anyone was in close contact with those cases,” Anderson said.

The slight increase in cases came as the number of visitors arriving in Hawaii topped 400 for the fifth day in a row. On Friday, 1,431 passengers arrived in Hawaii, with 458 of them visitors, despite a mandatory two-week quarantine for arriving passengers, according to numbers released Saturday by the Hawaii Tourism Authority. Gov. David Ige has said he will provide more information this week about when he will end the trans-Pacific passenger quarantine.

Anderson said he was less concerned about the demonstrations and more concerned about people lowering their guard and relaxing to the point where they’re no longer following physical distancing measures, wearing masks, and washing hands.

“The reason we’re doing so well in Hawaii is because of the strict adherence to those recommendations … people are compliant,” he said. “The worst problem we’ve had in Hawaii has been associated with people who have gone to work sick and they’ve infected lots of people.”