Dr. Brendan Hanley said Monday that about 45 per cent of Yukoners have received the flu vaccine to date. (CBC)

The Yukon's current wave of swine flu could start slowing down, now that a large portion of the population has been vaccinated, the territory's medical health officer said Monday.

Dr. Brendan Hanley said the Yukon is seeing a steady increase in swine flu infections, but there were no new hospitalizations in the past week.

But Hanley told reporters in Whitehorse that while it's too early to say whether flu cases have peaked in the territory, the present wave could ease up as a result of a territory-wide vaccination program now in its third week.

"Our wave might well be moderated by an increasing number of vaccinated people," he said.

About 45 per cent of Yukoners have received flu shots since the vaccination campaign began Oct. 26.

The H1N1 virus began spreading in the Yukon in mid-October. A young girl from the territory died Nov. 1 from complications related to the virus, although health officials say she had an underlying medical condition.

Hanley said the current wave of the flu is the first for the Yukon, unlike other parts of Canada, which are experiencing a second wave.

"Given that it's very early in the flu season, we could easily have another wave in the new year," he said.

While health officials are monitoring the spread of swine flu in the Yukon, they are also keeping a close watch on closed facilities such as the Whitehorse Correctional Centre, where several inmates with flu-like symptoms have been isolated.

"This is a crowded facility and it's a place where you have, as we all know, many more residents then were designed for the facility," Hanley said.

"So it doesn't make it necessarily easy, for instance, in the short term to set up a separate isolation area. … That did happen in a very short period of time,within hours, actually."

Hanley said inmates who are not infected with the H1N1 virus are being given Tamiflu as a preventive step.

The distribution of Tamiflu will be limited to the jail and other closed facilities, such as a long-term care home, should the need arise, he said.