"We anticipate that he will be available to play in the third Vodafone men's Ashes Test at the MCG in Melbourne.
"Cummins is understandably very disappointed not to be able to captain Australia for the day-night Test in Adelaide.
"Steve Smith will captain the team in Cummins' absence. Michael Neser comes into the playing XI to make his Test debut and Travis Head will be vice-captain.
"Mitchell Starc and Nathan Lyon were dining at the same restaurant as Cummins but at a separate table outdoors. SA Health has deemed them casual contacts and they are free to play."
Speaking on SEN, cricket reporter Peter Lalor said Australia were "very lucky" Starc and Lyon would be able to play.
Lalor explained that Cummins was eating at the table next to a man who received his positive result while eating.
It clears the path for Smith to captain Australia for the first time since the infamous Cape Town sandpaper-gate Test in 2018.
It was reported when Smith was announced as Cummins' deputy that if the quick was to miss a game, the former skipper was in the box seat to take over the captaincy.
At the time, Cummins was asked what would happen if he rested due to his bowling workload.
"I very much doubt if I'll rest from Test cricket," Cummins said. "I've never rested from a game of Test cricket and I doubt if I'll start now."
However, Smith did have a taste of leading again in Brisbane last week as Cummins revealed his deputy stepped up when needed — and played a crucial role in the fast bowler dismissing Ben Stokes in the second innings.
"I was going to bowl Starcy one more, and Smithy kind of tapped me on the shoulder and said 'I think it's your turn'," Cummins explained.
"I went up to (Smith) and gave him a big high-five. He was a big part of that wicket."
Smith revealed the pair were taking a collaborative approach.
"We're talking. Patty is making the decisions, but we're talking and communicating," Smith told Fox Cricket. "I get a point across, and he makes a decision … there's plenty of communication there."
Cummins' Covid drama has caused a double change to Australia's bowling line up, after Josh Hazlewood was ruled out through injury.
Michael Neser, who has two ODI caps and has been on the verge of making his Test debut for the past 18 months, will get his first baggy green, while Jhye Richardson was selected to replace Hazlewood.
Australia also comes into the match with an injury cloud over David Warner, who Cummins admitted was still being bothered by his bruised ribs.
"He'll be right, he had a bat yesterday, batted with some discomfort, but knowing Davey, he's not going to miss this one," Cummins said on Wednesday afternoon
"He'll be fine when the adrenaline kicks in.
"It's one thing batting in the nets, different thing with a packed crowd.
"He didn't have painkillers, he's played close to 90 Tests. I'm sure a lot of them have been played with discomfort or things going into the game."