Tom Hanks and Rita Wilson announced that they tested positive for the novel coronavirus last week

Tom Hanks and Rita Wilson are “doing very well” a week after testing positive for the novel coronavirus, a rep for Hanks tells PEOPLE.

The married couple remain under quarantine at their home in Australia after being released from a Queensland hospital on Monday.

“Tom and Rita are doing very well and continue to recover,” Hanks’ rep Leslee Dart says. “Their recovery is very much on course for healthy adults with this virus. They are feeling better each day.”

Hanks and Wilson, both 63, were among the first high profile celebrities to reveal that they had contracted the coronavirus, formally known as COVID-19. As of Thursday, the rapidly spreading illness had infected 235,404 and killed 9,785 worldwide, according to Johns Hopkins University.

“Hello, folks. Rita and I are down here in Australia. We felt a bit tired, like we had colds, and some body aches. Rita had some chills that came and went. Slight fevers too,” Hanks wrote in a March 11 Instagram post. “To play things right, as is needed in the world right now, we were tested for the Coronavirus, and were found to be positive.”

The Forrest Gump actor had been on Australia’s Gold Coast for the pre-production of Baz Luhrmann’s untitled Elvis Presley biopic, in which he plays the music icon’s longtime manager Colonel Tom Parker. Filming for the movie has been halted following his diagnosis. Hanks is the only person on set believed to have tested positive for the virus, according to a representative from the film in Australia.

The day after first announcing their diagnosis, Hanks posted an update on how he and Wilson were doing.

“Hello folks. @ritawilson and I want to thank everyone here Down Under who are taking such good care of us,” he wrote alongside a photo of the couple in a hospital. “We have Covid-19 and are in isolation so we do not spread it to anyone else. There are those for whom it could lead to a very serious illness.”

“We are taking it one-day-at-a-time. There are things we can all do to get through this by following the advice of experts and taking care of ourselves and each other, no? Remember, despite all the current events, there is no crying in baseball,” he continued, referencing his famous line in A League of Their Own.

Hanks recently posted another update on his and Wilson’s condition on Wednesday, noting that their symptoms were “much the same.”

“Hey folks. Good News: One week after testing Positive, in self-isolation, the symptoms are much the same. No fever but the blahs,” Hanks wrote in both Twitter and Instagram posts. “Folding the laundry and doing the dishes leads to a nap on the couch. Bad news: My wife @ritawilson has won 6 straight hands of Gin Rummy and leads by 201 points.”

As information about the coronavirus pandemic rapidly changes, PEOPLE is committed to providing the most recent data in our coverage. Some of the information in this story may have changed after publication. For the latest on COVID-19, readers are encouraged to use online resources from CDC, WHO, and local public health departments and visit our coronavirus hub.