The Directorate of Health has issued a helpful and informative FAQ about the coronavirus which will hopefully allay many of your concerns.
Amongst the questions answered is that you can indeed be tested for coronavirus, or 2019-nCoV as it is medically known, in Iceland but you should not ask to be tested unless you display the symptoms. Health and civic authorities are stepping up preparations, but there are as yet no travel restrictions, although travel to affected areas is not advised. Furthermore, there is as yet no entry screening for the virus.
To avoid contraction, the Directorate advises practicing basic good hygiene, i.e. “hand washing/sanitizer before eating, after touching common surfaces, after cough/sneeze/touching the face or cover the nose and the mouth when coughing/sneezing”. You should also avoid contact with the sick and visiting places where live or dead animals are handled. Those who have traveled to affected areas in the past 14 days are advised to contact email@example.com.
The FAQ also emphasises quite clearly that you cannot contract 2019-nCoV from packages sent from China. Although not included in the FAQ, it should also be mentioned that face masks are actually designed to prevent you from spreading disease to others; their ability to prevent you from catching a virus is not very reliable.
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