The heir to the throne has also spoken to his mother, Queen Elizabeth, 93, who has been self-isolating at Windsor Castle since last week.
Charles was last with his sons William and Harry in public on March 9 at the annual Commonwealth Service at Westminster Abbey. The event marked Harry and wife Meghan Markle’s last official royal event in the U.K. before they officially step down as senior working royals on March 31.
Charles and his wife Camilla, Duchess of Cornwall have been self-isolating at Birkhall, their home on Queen Elizabeth’s Balmoral estate in Scotland. Following Charles’s positive diagnosis on Tuesday, Camilla moved to another area of the estate to self-isolate.
“Both of them remain in good spirits,” a palace source tells PEOPLE. “There is a sense of keeping calm and carrying on. The duchess is concerned for him but she is aware of his own good spirits and therefore is keeping a close eye on him and mindful of her own situation. She is upbeat.”
Last week, Queen Elizabeth left her Buckingham Palace home in London for Windsor Castle amid the coronavirus outbreak. There, she was reunited with husband Prince Philip, 98, who had been staying on the couple’s Sandringham estate since late last year following his hospitalization.
Kate Middleton, Prince William and their three children — Prince George, 6, Princess Charlotte, 4, and Prince Louis, who turns 2 in April, are believed to be staying at their Sandringham country estate, Anmer Hall, which is about 110 miles north of London in Norfolk.
After leaving the U.K. earlier this month, Meghan Markle and Prince Harry returned to Vancouver Island in Canada to reunite with baby Archie, who stayed behind while his parents wrapped up their official royal engagements before their royal exit earlier this month.
The Duke and Duchess of Sussex spoke out about the need to support each other through the coronavirus outbreak in a post on Instagram.
“These are uncertain times. And now, more than ever, we need each other. We need each other for truth, for support, and to feel less alone during a time that can honestly feel quite scary,” they wrote. “There are so many around the world who need support right now, who are working tirelessly to respond to this crisis behind the scenes, on the frontline, or at home. Our willingness, as a people, to step up in the face of what we are all experiencing with COVID-19 is awe-inspiring. This moment is as true a testament there is to the human spirit.”
Can’t get enough of PEOPLE‘s Royals coverage? Sign up for our free Royals newsletter to get the latest updates on Kate Middleton, Meghan Markle and more!
Prince William also shared a personal video message amid the coronavirus crisis last week, saying: “Whenever and wherever adversity strikes, the people of the U.K. have a unique ability to pull together. The way that local communities support those affected shows the very best of our values and human nature.”
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.