Hawaii on Wednesday saw the largest increase in coronavirus cases yet — 34 — but state officials acknowledged that more records likely are on the way despite travel restrictions and other measures implemented to stem the tide of disease.

How bad could it be?

A University of Washington study says Hawaii could see 372 deaths by July, with a peak of 12 deaths a day starting May 1 and lasting through the first week of May.

The study, which made projections for all 50 states, was cited by the White House on Tuesday when it said the United States should brace for 100,000 to 240,000 deaths from coronavirus.

In their Hawaii report, updated Wednesday, the University of Washington researchers predicted that Hawaii’s health care system could be overwhelmed if the state doesn’t increase its hospital bed capacity. The study said the islands could experience a shortage of 125 ICU beds and 178 regular beds at the peak of the health crisis.

Questioned about the study Tuesday, Gov. David Ige said he felt the projections were off-base because they fail to take into account Hawaii’s 14-day quarantine for travelers, which was expanded Wednesday to cover those going between islands.

Wednesday’s new tally boosted the number of COVID-19 cases in Hawaii to 258.

“We fully expected to see an uptick in the cases,” state Health Director Bruce Anderson said at a news conference. “What we’re seeing now is a shift from cases which are imported — travelers or people who came in contact with travelers — to cases where there is no travel history.”

Asked when the outbreak would peak, Anderson said officials are looking at a number of models that range from a few weeks to a few months.

“It’s almost impossible to predict at this point in time,” he said. “We’re still early on in our course of the epidemic in Hawaii. I expect it will get worse before it gets better.”

Ige said the U.S. Army Corps of Engineers has completed an assessment of sites on Oahu that could serve as temporary hospitals, including the Hawai‘i Convention Center, and is now examining sites on the neighbor islands.

In addition, the state is monitoring daily the state’s hospital-bed capacity and supply of medical equipment such as ventilators.

So far the crisis hasn’t reached the level at which it would trigger the construction of a temporary care facility.

“But we are constantly monitoring the utilization of (hospital beds and supplies) and we would be looking to establish something as we approach critical (stages),” the governor said.

The state also could establish tent-based care facilities if need be, he said.

Anderson urged Hawaii’s population to continue following the governor’s social distancing mandates to allow health investigators a better chance of tamping down the epidemic as it takes hold in the community.

Meanwhile, the mother of the Waikiki bartender currently on life support because of COVID-19 also has tested positive for the disease.

Peggy Torda-Saballa, the mother of Lee-Jacob “Coby” Torda, said she received her result Wednesday via phone after getting tested on Saturday.

“I was taking care of my son when he was sick, so I had very close contact, so it doesn’t surprise me in the least,” Torda-Saballa said.

Torda-Saballa said she began experiencing the symptoms of COVID-19 about three days ago, but they have been mild.

“I did run a fever (Tuesday) — it was just one day,” she said. “And I had lost (my) taste and smell senses for the last three days now, and I have a little of a dry cough. That’s it.”

Torda was taken to Kaiser Permanente’s Moanalua Medical Center on March 21 after experiencing severe symptoms of the disease, including a high fever, coughing and headaches. He started experiencing his symptoms on March 9.

State officials also announced that the state’s first and only COVID-19 fatality likely caught the disease in Las Vegas and brought it back with him to Hawaii.

On Tuesday, Ige and health officials announced the state’s first coronavirus-related death, an “older” Oahu man with underlying health conditions who died Monday night.

No other details were disclosed Wednesday, except that the victim had recently visited Las Vegas, an area where transmission of the coronavirus has been active.

“We are sending a specimen to our state lab for testing but we expect the results to remain positive,” Anderson said.

Elsewhere, a state Department of Human Services employee, a Honolulu postal worker and a downtown office worker tested positive for COVID-19, according to reports Wednesday.

In a memo to DHS employees, the department said it was notified Wednesday afternoon that a DHS employee tested positive for COVID-19 and the Department of Health is providing guidance.

“The employee was already on self-quarantine since March 22, 2020, and the work area has been sanitized. Staff that may have been exposed to this employee have already been notified,” Deputy Director Cathy Betts wrote in the memo.

According to the U.S. Postal Service, its worker is an employee of the Honolulu mail processing and distribution facility.

“We are in the process of reaching out to local public health officials and will follow the guidance they provide,” the USPS said in a statement. “We believe the risk is low for employees who work at the Honolulu mail processing facility, but we will keep our employees apprised as new information and guidance becomes available.”

The USPS added that “out of an abundance of caution, we are enhancing and supplementing our current cleaning protocols using disinfectants within the mail processing facility.”

The Centers for Disease Control and Prevention, the World Health Organization and U.S. Surgeon General have said there is currently no evidence that COVID-19 can spread through the mail and packages and that the risk is minimal.

A worker in the 25-story downtown office building Bishop Place also tested positive for COVID-19, a fact that prompted Douglas Emmett Management to notify the other building tenants.

The management company said in a memo that it learned of the positive test on Tuesday, and said the worker has not been in the building at 1132 Bishop St. since Friday.

“We have also been informed that as a precautionary measure, the individual’s co-workers have been told to isolate for two weeks and are also no longer working at Bishop Place,” according to the memo, which does not identify the office involved.

The company said it already had increased cleaning protocols in the building but would immediately hire a professional cleaning service “to again clean and disinfect all common areas in the building.”

Tenants in the building include the U.S. Bankruptcy Court and the offices U.S. Rep. Ed Case, who represents urban Honolulu.

“My Capitol Hill and Honolulu staff and I have largely been on telework for two weeks,” Case said in a written statement Wednesday. “We’ve had one person in each location to maintain in-office operations and handle needs.”

“We are awaiting further specifics to determine whether those that have been here have been or will be at risk. Once we have that information, we’ll determine whether the best medical advice is that we should further modify my district office operations,” Case said in the statement.

Staff writers Mark Ladao and Kevin Dayton contributed to this report.