The England support staff and family members who have tested positive are in isolation.
The World Test Championship playing conditions allow for players that test positive to Covid-19 to be subbed out with a like-for-like replacement – similar to a concussion substitute.
On Monday morning, the England players and staff were told to stay in their hotel following a positive test result among the family group. The players underwent rapid tests before they were given the all-clear to leave the hotel and make their way to the MCG.
Twenty minutes before play was scheduled to get underway on day two, Cricket Australia confirmed four members of the England camp had tested positive to Covid-19 – two support staff and two family members – but the Boxing Day Test was allowed to continue.
Earlier this year, the fifth Test between England and India at Old Trafford was postponed after four members of the India support staff tested positive to the virus.
Australia and England players are operating under Level 4 biosecurity protocols, which prevents them from eating indoors and attending bars. However, CA would be reluctant to strengthen the protocols for the remainder of the tour after England's cricketers voiced their concern about bubble fatigue.
"We don't want to completely lock down the players," CA chief executive Nick Hockey told reporters at Adelaide Oval last week.
"We're very conscious of taking a proportionate approach, very conscious of their mental wellbeing … but equally, we're minimising the risk of (players) coming into contact with positive cases.
"The alternative would have been to lock everyone down completely for the whole tour. We've learned over the last 18 months that's got other consequences in terms of mental health and wellbeing."
The fourth Test is scheduled at the SCG from January 5, while the final match will be played in Hobart the following week. But the Covid-19 situation in Sydney is considerably worse than Melbourne — NSW recorded 6324 new cases on Monday, while Victoria registered 1999.
While close contacts in Victoria are released from isolation as soon as they produce a negative swab, in Sydney and Hobart they need to isolate for seven days – a rule that thwarted Australian captain Pat Cummins in Adelaide earlier this month.
However, News Corp reported that NSW Health could adopt Victoria's rules before the SCG New Year's Test gets underway.
Regardless, former England captain Michael Vaughan led calls for the final three Tests to all be staged at the MCG to reduce the risk of Covid-19 ruining the series.
"I think Cricket Australia have to act quickly and be proactive in terms of the situation. It's unprecedented times," Vaughan told Fox Cricket.
"Could the next Test match be played here in Melbourne, under lights at the MCG, to make sure we all stay in Victoria where the protocols are different to Sydney?
"Do we really want to risk taking two teams over to Sydney, broadcast and production staff? You get to the SCG, there's one case in the team on day one and the Test match is off.
"Surely Cricket Australia have to be proactive and realise that it's not going to be easy (even) staying here with what we've seen this morning."
Meanwhile, the media had a Covid-19 scare of its own in Melbourne, with Channel 7 forced to make several changes to its commentary team after a member of its broadcast staff tested positive to Covid-19 on Sunday night.
Multiple high-profile commentators were required to take Covid-19 tests on Monday morning and isolate until they received a negative result.
Channel 7's roster of callers was completely different from the previous day, with the Big Bash crew replacing the likes of Ricky Ponting, Glenn McGrath, Alison Mitchell and Ian Botham.
Despite the Covid-19 drama on day two of the Melbourne Test, Hockley was adamant the $100 million series would go ahead as planned.
"I can't tell you the amount of work going on behind the scenes," he told reporters at the SCG on Monday.
"The diligence of our medical team and players, the diligence with which they're working through each of the protocols is extremely impressive.
"That's not part of our current planning. We are very focused here on making sure that we can play the full Boxing Day Test, and that we can move them safely by charter to Sydney for the New Year's Test."