After days of intensive searching across the state, utilising every Tasmania Police resource at their disposal, police had their man.

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The 44-year-old was bailed up "without incident" during a police check at a Waverley home, and currently sits in custody awaiting interview as an investigation into an incident that left a man dead and a woman critically injured presses on.

Hours after he was arrested, a woman, who police allege is his victim, was discharged from the Launceston General Hospital, a week after she was rushed there with critical wounds.

She was instantly reunited with her children, who police say witnessed the alleged stabbing, and they began piecing back together the past week of their lives.

That is according to Tasmania Police Detective Inspector Mel Groves, who, fronting media for the third time in four days, said the family would be on a long road to physical and psychological recovery.

"[The woman] can be reunited with her family and they can begin this healing process together," Detective Inspector Groves said.

"She's progressing well from her recovery, from the physical injuries, and with the psychological injuries, like her children, we'll be providing ongoing support through other agencies to help them with their psychological recovery from this incident.

"The children are relieved in relation to this incident and they are very excited to be reunited with their mother and to know they can see her physically recovering from her injuries."

Detective Inspector Groves said informing the victims the alleged 44-year-old man was in custody was "reassuring".

"It alleviates one of their concerns. It's that long road to recovery for them, but I'm comfortable [the woman] will make a full recovery both physically and psychologically in the long-term," she said.

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The arrest came just seven hours after Tasmania Police made a radical move to introduce a $50,000 financial incentive for any information leading to the arrest of the man they believed to be the perpetrator of the Ravenswood incident.

The announcement was made by Northern District Commander Stuart Wilkinson who detailed irregularity of offering a reward in a search.

But Detective Inspector Groves could not confirm or deny whether or not the reward had been the missing piece in the search puzzle.

"One of the fundamental things behind Crime Stoppers is the right to provide information anonymously. So I can't disclose whether it had anything to do with anything relating to this male's arrest," she said.

Detective Inspector Groves was unable to provide much in the way of details about the investigation as police continued to compile evidence.

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