Meanwhile, one of the victims is recovering in the intensive care unit at the Royal Brisbane and Women’s Hospital after enduring 18 hours of reconstructive surgery to her injured right leg.

Fisheries Queensland said both creatures were caught on a single drum line on Saturday in the Cid Harbour area, near Whitsunday Island off the north Queensland coast.

"One measured 3.3 metres and the other was over 2 metres," the Department of Agriculture and Fisheries said in a statement.

"While sharks of this size are potentially very dangerous to humans, it is unclear if they were responsible for injuries caused to two swimmers this week.

"The shark carcasses will be towed well out to sea for disposal."

The rollout of the baited drum lines and shooting of sharks was announced in response to the two near-fatal attacks on Wednesday and Thursday afternoon in Cid Habour.

Melbourne schoolgirl Hannah Papps, 12, remained in a critical but stable condition in the Lady Cilento Children's Hospital after being given life-saving first aid on a boat.

Tasmanian tourist Justine Barwick, 46, was in a stable condition in the Royal Brisbane and Women's Hospital after being mauled in the 24 hours prior to Hannah's attack.

Ms Barwick's husband, Craig, issued a statement on Saturday afternoon saying his wife was recovering after a marathon surgery.

"The surgery took much longer than we were anticipating finishing at 1:00 this morning," he said.

"During the surgery specialists repaired ligaments and other structures including nerve, skin and
muscle grafting to reconstruct the injured limb.

"It looks like they have done an amazing job, it looks like it has always been there."

Hospital specialists plan to reduce the level of Mrs Barwick's sedation during the next 24 hours.

"The current prognosis is looking good with an estimated 2-3 weeks recovery in Brisbane and then
back to Tasmania for further rehabilitation," Mr Barwick said.

"Justine has been opening her eyes and blinking in response to mine and Lynne's voice.

"All of us would like to thank the Surgical team for their marathon effort save Justine's leg."

Catching two sharks on the one line was "unusual", according to the department, which said the hooks would remain in place over the next week and reviewed regularly.

"The use of drum lines removes large dangerous sharks from a specific area and reduces the risk to people," the department said.

The Fisheries Queensland advice to swimmers was to go into the water in patrolled areas, never swim alone and not to swim near schools of fish. The department also advised against swimming in murky water and to never swim after dusk, at night or before dawn.

Bond University associate professor of environmental science Dr Daryl McPhee said there was "no easy solution" to these situations.

"I reviewed all of the shark deterrents for New South Wales a couple of years ago," he said.

"There was no easy solution, no off-the-shelf solution for all situations."

Dr McPhee said two shark attacks in 24 hours was unusual but not unheard of, and did not believe the same shark was responsible for both attacks.

"Most sharks eat a range of prey. They don’t get a taste for humans or anything like that," he said.

Great Barrier Reef Marine Park Authority assistant director of reef conservation action Mark Read said sharks generally did not hunt humans in the water.

"There certainly seems to be a variety of reasons why sharks interact with people in the water," he said.

"Territory is one, because they feel threatened and respond with a bite, and also sharks are curious animals and often check things out using their teeth.

"People often have strong opinions on the value of sharks.

"Sharks are a key component of the marine and estuarine regions.

"If you remove sharks, there will be considerable problems for the remaining species ... and they have very deep connections to the traditional owners."

- with Luke Sayer and AAP