A 38-year-old man being treated for Crimean-Congo haemorrhagic fever at the Royal Free London NHS Foundation Trust has died.
He was then transferred to the Royal Free London NHS Foundation Trust. Tests revealed he flew into Scotland from Dubai, although his journey originated in the Afghan capital, Kabul.
It was the first recorded case of the deadly disease in the UK. Other passengers who sat close to him on an aircraft are undergoing daily health checks.
The health board said two of them - one who remained in "close proximity" to the ill man during the flight - will be monitored on a daily basis for the next two weeks for any developments of relative symptoms.
The other two passengers do not require follow-up surveillance and the risk to all other passengers on the flight from Dubai is "extremely low", it added.
In a statement, the board said: "In total, therefore, we are currently following up two passengers from the flight with daily monitoring as a precaution for two weeks - two weeks is the maximum incubation period for the disease."
"Crimean-Congo haemorrhagic fever can be acquired from an infected patient only through direct contact with their blood or body fluids, therefore there is no risk to the general public," the Royal Free London NHS Foundation Trust said.
"We would like to extend our condolences to his family."
Congo fever is a tick-borne viral infection and is fatal in 30% of human cases. It causes large areas of severe bruising, nosebleeds and uncontrolled bleeding at needle injection sites.
Early symptoms include headaches, fever, vomiting and back, joint and stomach pain. They can also include red eyes, red spots on the roof of the mouth and jaundice.
The virus is widespread in parts of Africa, Asia, India and the Middle East.
:: Anyone who is worried they may have the disease should contact NHS24 for advice on 08000 858531.