The virus is gradually dismissing each member of the Black Caps squad.
Conway endured a five-wicket defeat to England at Trent Bridge, now he must mull over the loss in London isolation alongside debutant Michael Bracewell.
Physiotherapist Vijay Vallabh and trainer Chris Donaldson are also infected.
The quartet will travel separately from the team to Leeds on Sunday.
The rest of the touring party will keep getting monitored for symptoms and tested in the gap between fixtures. Captain Kane Williamson has rejoined the squad after his bout.
Coach Gary Stead said the situation is the reality of touring during the pandemic.
"Michael's obviously been a close contact of everyone else.
"It's unfortunate for him, but the symptoms are mild, he's feeling good and he'll be out of isolation when we start training again at Leeds."
Meanwhile, Blair Tickner and Dane Cleaver are due to replace the injured Kyle Jamieson and Cam Fletcher.
That prompted Stead to raise the question about whether Jamieson, who was diagnosed with a stress tension in his lower left back, should have been replaceable a la concussion or Covid rules.
"We were hampered, given it was genuine and halfway through out first bowling innings.
"Perhaps that's something that could be looked at, although we don't want to get to the point of big squads and people abusing the spirit of the game."
Stead was also asked whether Lockie Ferguson's an option to play tests after achieving Indian Premier League glory with Gujarat.
"We haven't considered Lockie at this stage, he hasn't played red-ball cricket for more than two years now.
"We didn't feel as though he was physically in a position to play and we wouldn't want to put him at risk.
"I wouldn't like to rule it out for the future though."
The team has moved to London for the next few days before assembling for the third dead rubber fixture.
Stead remains unshakeable in the world champions' approach.
"We have trust in our players, and in how we're playing the game. We just need a bit of luck. Both tests we've been in the game until the last session but failed to pick up a wicket when we needed to."
And was Stead daunted by a crowd that inspired the hosts as a virtual 12th man?
"We've experienced it on a number of occasions. It happened at Lord's, it happened here and the [2019] World Cup final. It certainly is a lift but we need to remember we're still out there competing, and that crowd can also be silenced."
