COVID-19 cases went up again this weekend and visitors coming to Hawaii rose despite a mandatory 14-day self-quarantine.

The new statistics are a concern for state and county officials who have ordered COVID-19 lockdowns aimed at reducing visitors and keeping residents’ mobility to a minimum.

The main goal is to flatten the new coronavirus curve. Officials still don’t have enough data to determine whether greater enforcement and more restrictions are needed.

Lt. Gov. Josh Green expects that the peak “will happen probably in the last five days of this month. … But I don’t yet know how many (cases) that is going to be.”

“In the end we’re going to have a handful of fatalities or a really large number, and by doing better social distancing … and quarantine measures … we stand to have a good chance to have the lowest mortality rate in the country.”

So far, COVID-19 has claimed four lives in Hawaii. However, there weren’t any new deaths Sunday, when health officials reported that 20 new cases had brought the statewide total to 371.

The state Department of Health said most new cases were introduced by travelers, especially Hawaii residents who had traveled. However, community-associated cases are now a greater concern. That’s why officials are paying attention to trans-Pacific and interisland passenger volume as well as compliance with social distancing requirements.

Mayor Kirk Caldwell issued a stay-at-home, work-from-home order for Oahu on March 22, followed by Gov. David Ige, who issued a stay-at-home order for the state on March 23. Both orders are in effect until April 30.

Since March 26, when Ige instituted a 14-day mandatory self-quarantine for all arriving trans-Pacific passengers, 1,476 visitors have come into the state. That quarantine was expanded Wednesday to interisland travelers, although data is not yet available for this group.

Violation of the rules during a state of emergency is a misdemeanor punishable by up to a $5,000 fine and one year imprisonment.

The Hawaii Tourism Authority reported that Saturday’s trans-Pacific passenger count had risen to 683, including a spike in visitors, which increased to 106. The number of visitors on Friday was 94, and it was 89 Thursday.

More flights came into the islands Saturday, too. There were 25 trans-Pacific flights as compared with 22 Friday and 20 Thursday.

While the visitor passenger count rose recently, it’s significantly below pre-COVID-19 levels. Normally, at this time of year, roughly 270,000 visitors would have come during the same period.

But greater dampening is wanted by some residents and officials, who fear that a single visitor arriving with COVID-19 could infect many people. On Sunday, Honolulu City Council member Kym Pine sent an open letter to airline operators with flights coming to Hawaii, calling on them to cease all nonessential travel to the state.

“Travel sites are promoting cheap airfares to Hawaii with only vague guidance on COVID-19 travel restrictions,” Pine wrote. “We need to protect Hawaii residents from further spread and spare our healthcare industry from an influx of out-of-state cases. Further, some of these arriving passengers have no lodgings booked, stressing our already- strapped facilities caring for the homeless.”

Honolulu police were out in full force Sunday shooing away visitors and residents who were hanging out on the sand at Sunset and Maunalua Bay beach parks. A city worker was doing the same at Sandy Beach Park.

But there wasn’t any enforcement at Ehukai Beach Park when at least 10 people were congregating on the sand, including a couple eating a plate lunch.

A local family, admiring horses from the fence line of a North Shore ranch, said they’d gone for a drive since the beaches are closed and there “wasn’t anything else to do.”

Judging from the amount of traffic on Oahu’s roads Sunday, more people seemed to be out and about than the exemptions would allow.

Twelve people were arrested between Thursday and Sunday on suspicion of violating emergency coronavirus laws, according to Honolulu police booking logs. Eleven were men and one was a woman. All were between the ages of 18 and 50. Most were also arrested in connection with other offenses, such as driving without a license, liquor violations or warrants.

On Sunday the Pacific Urban Resilience Lab released the results of an electronic survey meant to provide insight into the community spread of COVID-19. The survey included results from 11,000 respondents during the last week of March.

The authors reported that nearly 25% of Hawaii residents surveyed feared they had symptoms of the new coronavirus. As many as 3% of respondents said they had attended gatherings with family and friends even after the Hawaii stay-at-home order began. Another 3% had returned from a trip within the last 14 days.

The authors did not provide a margin of error for the survey.

Karl Kim, professor of urban and regional planning at the University of Hawaii, said in a statement, “There are many serious ‘distancers’ but there are also potential ‘spreaders’ who continue to go to work or to gatherings with family and friends.”

Green said that overall, people are doing a good job with social distancing, though he’s “certainly seen moments that are failures, and I’ve been a part of them.”

“The biggest concern I have is people being too close to one another in long lines,” Green said, adding that another issue is that activity exemptions are too broad.

“Tightening those exemptions and being tougher at some public places would help,” he said. “If everyone just took the most conservative tack, even if they have an exemption, and stayed home most of the time, that would do it. … What we do will affect our neighbors.”

Star-Advertiser reporters Rob Shikina and Mark Ladao contributed to this story.