However the health board is expected to come under pressure over the next two weeks.
Ms Evans spoke to the BBC's Good Morning Scotland radio programme today (Saturday).
Asked about the situation in her health board area, she said: "What a difference a week has made for us.
"Certainly, a slowing down of those infection rates that we saw in just in the run-up to Christmas and at the start of New Year."
Ms Evans said the effect of the Omicron wave would still be felt in hospitals around Scotland.
She said: "The baked-in cases that we've got, we expect to see for the next week, two weeks.
"So that means that we're still under pressure in health and social care systems, but it gives us some cause for optimism.
"Particularly when you start to look at the effects elsewhere in Scotland and the UK and in other parts of the world where the Omicron wave happened sooner, we're starting to see a slowdown or even a plateauing of hospitalisations.
"So that's positive news, but we're nowhere near out of the woods yet."
Health Secretary Humza Yousaf said on Friday that the Omicron wave appeared to be "decelerating" but more data was needed to be definitive.
On Thursday, the Scottish Government's daily coronavirus figures included both PCR and lateral flow test numbers for the first time.
This was due to a change in the rules where a positive lateral flow result no longer needed a PCR confirmation.
Ms Evans also expressed some concern over whether everyone would report their lateral flow tests.
She told Good Morning Scotland: "We call it losing sight of the case burden. That's a real worry."
She added: "I think we all benefit from registering those results and my plea would be do that, absolutely do that.
"Particularly with the dominance of lateral flow testing now."