Australia captain Pat Cummins will remain in Sydney to be around his seriously ill mother, ruling himself out of the fourth and final Test against India in Ahmedabad.

Cummins returned home after Australia's second Test defeat in Delhi to be close to his family, with mother Maria placed into palliative care.

Steve Smith stepped in as skipper for the third time since Cummins became Test captain in November 2021 for Australia's famous nine-wicket win in Indore last week.

The team checked in with Cummins after the memorable victory at Holkar Stadium on Friday, as Australia celebrated just their second Test win on Indian soil in 19 years.

Cummins is still captain for Australia's three-match ODI series in India, starting on March 17, but it appears likely he will miss those white-ball matches, too.

Australia on Monday also announced Tasmania quick Nathan Ellis would replace Jhye Richardson in the ODI squad after the Western Australian hurt his hamstring.

Meanwhile, Todd Murphy received a special mention from Smith after the win in Indore despite fellow spinners Nathan Lyon and Matt Kuhnemann taking all the wickets.

Lyon put in a legendary performance to take 11-99 for the match in Indore, while Kuhnemann grabbed his first five-wicket haul in just his second Test.

Murphy, who had a slight side injury after the second Test loss in Delhi, finished across India's two innings with figures of 1-41, which seemed unremarkable on the face of it.

But it was the 22-year-old's ability to keep bowling tight when wickets weren't coming, as they were during his seven-wicket haul on debut in Nagpur, that seriously impressed.

Australia assistant coach Daniel Vettori, New Zealand's greatest spinner, said Murphy's performance in just his third Test had not gone unnoticed.

"Steve Smith singled him out around his performances in the last Test," Vettori said on Monday.

"His spell allowed everyone around him to take those wickets.

"The fact that (Virat) Kohli had never been stumped before that Test match in Delhi when Murphy got him out.

"I think Todd has that skill that he can be a defensive bowler and he can be an attacking bowler and work around pretty much whatever is required from him in the game.

"For such a young spinner, and inexperienced spinners as well, he hasn't played that much first-class cricket to be able to come here and handle these tough situations and perform the role that's required has been impressive."

Vettori was also full of praise for Lyon and Kuhnemann, with Australia's three spinners performing above expectations during the Border-Gavaskar series.

Before the second Test, Australia had played three frontline spinners in the same match just twice this century.

Ravichandran Ashwin and Ravindra Jadeja are two of the greatest spinners of all-time, particularly in Indian conditions, but Australia's trio have hardly been outshone.

Lyon bounced back from a disappointing opening Test in Nagpur to have two of the best matches of his career in Delhi and Indore.

"Ever since I've started watching Lyon bowl I've marvelled at him," Vettori said.

"As a fellow finger-spinner who can't do what he did, there's always that element of his ability to bowl that ball which is so impressive.

"We saw him at his absolute best in this Test."

Australia will leave Indore on Monday for Ahmedabad ahead of the fourth Test, starting on Thursday at the 132,000-seat capacity Narendra Modi Stadium.