The two-time Oscar winner is easily the most famous person yet to disclose they have COVID-19, which the World Health Organization has declared a pandemic.
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Hanks said he and Wilson had felt tired, with colds, aches and slight fevers. "To play things right, as is needed in the world right now, we were tested for the coronavirus and were found to be positive," he said, adding they'll be "isolated for as long as public health and safety requires."
Australian officials said the couple were being treated at a Queensland hospital. "We wish them a very speedy recovery," state Premier Annastacia Palaszczuk told reporters.
Later Thursday night, Hanks tweeted an update with a photo of himself and Wilson, thanking the medical team in Australia treating them. They remain in isolation.
"There are those for whom it could lead to a very serious illness. We are taking it one-day-at-a time," he wrote, ending with "Remember, despite all the current events there is no crying in baseball."
Hanks had been in Australia shooting an untitled Elvis Presley biopic directed by Baz Luhrmann. Hanks plays Presley's manager, Colonel Tom Parker. The film, slated for release in October 2021, has suspended production, Warner Bros. said.
Hanks, after accepting the Cecil B. DeMille Award at the Golden Globes this year, spoke backstage about taking on the Parker role. "I will then finally have an answer to all these stupid questions about why I never played a bad guy," he said as the room burst into laughter.
Hanks and Wilson, both 63, were married in 1988. In 2013, Hanks disclosed he has Type 2 diabetes.
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Chet Hanks later posted on social media that his parents were doing fine and thanked fans for their concern.
Their other son, Colin, also noted that the family is "grateful for the outpouring of support."
Wilson had performed at the Sydney Opera House on Saturday night and earlier last week in Brisbane.
Queensland health authorities would not give specifics on their health due to privacy issues. But the state's update on its coronavirus infections describe a U.S. couple of their age both in stable condition.
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Palaszczuk said people who had been in close contact with Hanks and Wilson will have to self-quarantine but she cautioned that people who had taken selfies with Hanks recently should not panic about contracting the virus.
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She said she had spoken to Luhrmann and conveyed his reassurances that he would comply with the government's health restrictions.
Australia has confirmed more than 120 cases of infection with the new coronavirus, with three deaths from COVID-19.
For most people, the new coronavirus causes only mild or moderate symptoms, such as fever and cough. For some, especially older adults and people with existing health problems, it can cause more severe illness, including pneumonia.
The vast majority of people recover from the new virus. People with mild illness recover in about two weeks, while those with more severe illness may take three to six weeks to recover, WHO says.