The man, who was the first Briton to have tested positive for coronavirus, is in an isolation unit at London's St. Thomas Hospital and officials are on tracking down all the people he had contact with, especially those he travelled with on his United Kingdom return flight.
"Whilst [sic] I have fully recovered, my thoughts are with others who have contracted coronavirus", he said in a statement.
The father said: "They said both my son and his mum had been in direct contact with a confirmed case of coronavirus and told us to stay at home".
A spokesman for NHS Brighton and Hove CCG added: "All other NHS services in Brighton and Hove are open as usual and measures are in place to ensure the safety of all patients and NHS staff while also ensuring services are available to the public as normal".
And two prisoners at HMP Bullingdon in Oxfordshire are being tested for the illness and are being held in isolation.
A sign is pictured on the door of the Deneway branch of the Warmdene Doctor's Surgery in Brighton.
A statement on the website for County Oak Medical Centre - operator of previously closed Warmdene and Carden surgeries - told patients that the facilities have been "extensively and rigorously cleaned throughout".
The report also mentioned that Briton Steve Walsh is one of the most high profile cases among Coronavirus who is believed to be a super spreader.
"It's good to be back with my family and I would ask you please to respect our privacy from this point on".
The Scouting Association confirmed to Yahoo UK Mr Walsh has not been to any scout meetings since his return to the UK.
Mr Walsh said he contacted Britain's state-run National Health Service (NHS) as soon as he realised he might be sick. "While I have fully recovered, my thoughts are with others who have contracted the coronavirus".
Meanwhile, Patcham Nursing Home in Brighton said it was still "closed to all visitors" after one of the infected Global Positioning System visited a patient there about a week ago.
A spokeswoman for the care home said no one was unwell and the closure was a precaution.
Prof Cosford said PHE was working to trace the small number of contacts of the two doctors, including a Brighton GP, who were among the four new cases announced on Monday.
Earlier, Dr Tedros Ghebreyesus, director-general of the World Health Organisation, described the outbreak as "a very grave threat for the rest of the world".