HALIFAX -- New Brunswick's COVID-19 projection models estimate there could be between 550 and 1,750 deaths in the province during the course of the pandemic.

The total depends on compliance with public health measures and the models say New Brunswick could have experienced 5,600 COVID-19-related deaths if it had not put any public health measures in place.

This figure comes from modelling released Thursday at a briefing in Fredericton. It refers to the number of deaths that could have occurred between the time the province had its first case and when a vaccine was found in 12 to 24 months, said New Brunswick Health Minister Ted Flemming.

"I want to do everything in my power to make sure we keep the numbers as low as possible," said Premier Blaine Higgs. "Together, we are already taking the steps to make the best-case scenario our reality."

There have been no COVID-19 deaths in New Brunswick so far and Flemming said the eventual number of deaths depends on New Brunswickers and the diligence they show in following the advice of public health officials.

"This pandemic will be defeated outside the hospitals rather than inside," Flemming said. "One death is one too many, but we must be realistic and expect that there will be deaths from COVID-19 in New Brunswick. Limiting the number of deaths requires that everyone follow the direction of the chief medical officer of health by staying home and maintaining physical distance from others when you have to go out."

Staff from the Department of Health, Public Health and the regional health authorities developed the pandemic modelling. The province says it was inspired by similar modelling released by the governments of British Columbia, Saskatchewan, Quebec and Ontario. It said it would revise the models as new information becomes available.

More detailed information about the modelling is available on the provincial government website.

Closing schools, parks, and eliminating non-essential services and travel while imposing strict guideline on physical distancing and self-isolation have all worked, said Dr. Jennifer Russell, New Brunswick's chief medical officer of health.

Russell urged people to continue staying at home, practising good hygiene by regularly washing their hands, cleaning surfaces that are regularly touched, and using proper coughing and sneezing technique.

"The message is simple: keep doing what you are doing," said Dr. Russell. "We cannot afford to let up, even for a moment. Get plenty of rest and avoid information overload."

Dr. Russell reported three new cases, all in the Fredericton region, which brings the province's total to 111.

Of the 111 cases, 62 are travel-related, 33 are close contacts of confirmed cases, six are the result of community transmission, and 10 remain under investigation.

Ten people have been hospitalized and five have since been discharged. Four of the five patients remaining in hospital are in an intensive care unit. To date, 53 people have recovered.

Higgs said the three new cases are all from the same family and one member of that family travelled to Ontario a little more than a week ago. He said he mentioned this information not to place blame, but to illustrate how easy it is to catch and spread the disease -- and why self-isolation and other preventative measures are so important in the absence of a vaccine.

Higgs also said the province is delaying the start of recreational hunting and fishing season by two weeks. The decision will be re-evaluated on April 30, he said.

"As a government, we are committed to doing everything possible to protect our citizens," said Higgs. "I am a fisherman and I love the outdoors. I know what this means, and I am hopeful conditions will change soon."

This is a developing story. It will be updated.