Hawaii’s counties could see stronger social distancing mandates, including possible curfews and check­points in Maui County, depending on how well residents observe social distancing guidelines to reduce the spread of COVID-19.

About two weeks into Gov. David Ige’s statewide “stay-at-home” emergency proclamation that has closed nonessential businesses and ordered residents to stay and work at home, residents have generally reduced their travel and maintained their distance from other people.

The state’s mayors are still urging the public to take social distancing guidelines — staying 6 feet apart and avoiding crowds — to heart, but they are considering more county-level mandates if needed.

Mayor Michael Victorino said Friday that he might establish for Maui County a curfew and vehicle checkpoints like those in place on Kauai.

“I think stricter rules may come down. I’m going to give everybody until Tuesday,” Victorino said. “I’m going to be watching very carefully. If numbers keep increasing and people still continue to go to the beach and congregate … then we may have to look at other methods of stricter rules, whether we’re talking curfews, whether we’re talking maybe even putting up checkpoints. I’m not sure at this point.”

Maui County has a small fraction of the 371 COVID-19 cases reported in Hawaii as of Sunday, but the county has experienced a spike recently, including nine new cases Friday and the first reported two cases on Molokai.

There were 43 cases in the county as of Sunday.

Victorino announced a stay-at-home and work-at-home order on March 22, the same day Honolulu Mayor Kirk Caldwell issued a similar order. A day prior to Victorino’s order, he closed all the county beaches and parks.

Since then he has seen “some success and some failure.”

“The failures have been people not using common sense, not trying to keep social distancing as part of the mantra,” he said. “They are just ignoring it and spending time together, having barbecues, having a few brews on the beaches. They are gathering when they should be social-distancing.”

Kauai Mayor Derek Kawakami on Friday said most people in the county understand the severity of the situation at hand. Kawakami has held off on adding to perhaps the strictest coronavirus- related orders in the state, including a curfew and increased enforcement against nonessential travel.

But he said people need to “react instinctively” instead of waiting for government mandates. On Saturday, Kawakami admonished people who are breaking quarantine rules and putting the community in danger.

“There are still individuals who are willing to sacrifice that to put their own selfish needs in front of the needs of our community,” he said in his daily video update. “These folks are COVID-iots, and it’s not going to be tolerated.”

The worst of the COVID-19 outbreak in Hawaii could still be weeks away, and proper social distancing could help the state brace itself for those days.

A University of Washington model projects the disease’s impact to peak in Hawaii at the beginning of May, when the state could see 12 deaths per day.

“If we’re going to fight this virus — and I don’t think we’re going to see the peak until the end of April, early May — we’re going to make sure that peak is less steep,” Caldwell said. “We don’t want to take it into a situation where we don’t have sufficient ICU (intensive care unit) rooms if they really need them.”

The state Department of Health reported 281 COVID-19 cases on Oahu as of Sunday.

Caldwell said early Friday afternoon that he was jogging in a normally busy Kakaako and Ala Moana area.

“I was really pretty pleased with what I’m seeing. Traffic was way, way down,” Caldwell said. “It was basically a ghost town down by Ward theaters and all (around) that area. … It’s somewhat sad to see all of it, but it shows that people are compliant for the most part.”

He said businesses are self-imposing regulations and that the public as a whole is helping enforce current rules, so there is no need for any additional mandates in Honolulu.

By one analysis, Hawaii has reduced its travel more than most states during the pandemic.

Unacast, a data company that is tracking the movements of individuals in the U.S. and using that data to assign grades to states, ranks Hawaii among the country’s leaders with respect to reduced travel.

Hawaii island Mayor Harry Kim had no issue with social distancing, but he wants to find a “balance” between social distancing policies and the well-being of people subjected to those policies.

Kim said that in the long run a “stay-at-home policy is … very, very detrimental to good emotional and physical health,” which could disproportionately affect seniors and those who live in high-rise buildings.

He said it is important that people are able to go outside to exercise, and will discuss which parks can be opened to promote outdoor exercise while still maintaining social distancing guidelines. State and county parks have been closed because of the COVID-19 outbreak.

Hawaii island, he said, is at an advantage because of its small population and large area. It has the lowest population density of all the counties, with fewer than 50 residents per square mile, according to 2011 figures from the Department of Business, Economic Development and Tourism. There are nearly 1,600 residents per square mile in Honolulu.