There has been one reported death, which was announced on Monday.
In a post on the trust's Facebook page, Tim Noble, medical director for the trust, said: "I am saddened to confirm that a patient who was being cared for at Doncaster Royal Infirmary, and who had tested positive for Covid-19, has passed away.
“The patient, who was in their 50s, had underlying health conditions.”
The number of UK deaths rose to 422 on Tuesday, a rise of 87 in one day.
Doncaster is now under lockdown following Boris Johnson’s order to stay at home.
All non essential stores are now closed, people are being told to work from home wherever possible, gatherings of more than two people are banned and people are only allowed out once a day for exercise – with the police able to enforce the rules.
In a televised statement on Monday evening, the prime minister ordered people to leave their homes only under a list of "very limited purposes".
He said people should leave home only to exercise once a day (alone or people you live with), to travel to and from work where "absolutely necessary", to shop for essential items and to fulfil any medical or care needs or to help a vulnerable person.
This includes moving children under the age of 18 between their parents' homes, where applicable. Key workers or those with children identified as vulnerable can continue to take their children to school
Even when following the above guidance, people should minimise the amount of time spent out of their homes and should keep two metres (6ft) away from people they do not live with.
The government is also stopping all social events, including weddings, baptisms and other ceremonies - but funerals attended by immediate family members are allowed.
SHOPS AND LEISURE
Premises such as libraries, non-essential shops, playgrounds, outdoor gyms and places of worship have been ordered to close.
Hotels, hostels, campsites and caravan parks must also close unless key workers need to stay there, or if other people staying there cannot return to their primary residence.
Parks will remain open for exercise but people are not allowed to gather in groups.
Community centres can stay open but only for the purpose of "hosting essential voluntary or public services" such as food banks or service for homeless people, the guidance says.
Retailers that will be allowed to stay open include:
Supermarkets and other food shops
Home and hardware stores
Laundrettes and dry cleaners
Businesses will still be able to take online orders and deliver items to people's homes.
These are the only shops open in the Frenchgate Centre
Sainsbury’s: Mon to Sat 7.30am (NHS workers) 8.00am-8.00pm, Sun 10.30am-4.30pm
Boots/Pharmacy: Mon to Sat 8.00am-5.30pm, Sun 10.00am-4.00pm
Superdrug/Pharmacy: Mon to Sat 8.30am-5.30pm, Sun 10.00am-4.00pm
Wilko: Mon to Sat 9.00am-5.00pm, Sun 10.00am-4.00pm
Poundland: Mon to Sat 8.00am-6.00pm, Sun 10.00am-4.00pm
WHSmith/Post Office: Mon to Sat 8.00am-5.30pm, Sun 10.00am-2.00pm (PO) 4.00pm (WHS)
Holland & Barrett: Mon to Sun10.00am-4.00pm
Savers: Mon to Sat 10.00am-5.00pm, Sun Closed
Ramshaws Butcher: Mon to Sun 10.00am-4.00pm
Doncaster Market remains open – but only stalls selling food and essential items are open. Shoppers will have to follow the rules on social distancing.
First South Yorkshire and Stagecoach are now running reduced timetables. Passengers are urged to avoid all non essential travel by public transport.
All rail services are also running on reduced timetables. All details of revised timetables are available at Network Rail. Passengers are urged to avoid all non essential travel by public transport.
LEISURE AND ENTERTAINMENT
Cinemas, theatres and leisure centres, including The Dome, are all closed.
Yorkshire Wildlife Park, The Keepmoat Stadium, Cusworth Hall, Doncaster Racecourse are all also closed.
All Doncaster Rovers fixtures have been suspended until at least April 30.
Coronavirus: the facts
What is coronavirus?
COVID-19 is a respiratory illness that can affect lungs and airways. It is caused by a virus called coronavirus.
What caused coronavirus?
The outbreak started in Wuhan in China in December 2019 and it is thought that the virus, like others of its kind, has come from animals.
How is it spread?
As this is such a new illness, experts still aren’t sure how it is spread. But.similar viruses are spread in cough droplets. Therefore covering your nose and mouth when sneezing and coughing, and disposing of used tissues straight away is advised.
What are the symptoms?
The NHS states that the symptoms are: a dry cough, high temperature and shortness of breath - but these symptoms do not necessarily mean you have the illness. Look out for flu-like symptoms, such as aches and pains, nasal congestion, runny nose and a sore throat. It’s important to remember that some people may become infected but won’t develop any symptoms or feel unwell.
What precautions can be taken?
Washing your hands with soap and water thoroughly. The NHS also advises to cover your mouth and nose with a tissue or your sleeve (not your hands) when you cough or sneeze; put used tissues in the bin immediately and try to avoid close contact with people who are unwell. Also avoiding touching eyes, nose and mouth unless your hands are clean.
Should I avoid public places?
The advice now is to avoid public places and any non-essential travel. Travel abroad is also being advised against for the next 30 days at least, and many European countries have closed their borders.
What should I do if I feel unwell?
Don’t go to your GP but instead use the NHS website that can tell you if you need medical help and what to do next.
When to call NHS 111
NHS 111 should be used if you feel unwell with coronavirus symptoms and feel you cannot cope on your own at home, have been in a country with a high risk of coronavirus in the last 14 days or if you have been in close contact with someone with the virus.