The phrase "severe illness" is correct and can be used in written English.
Example sentence: The patient experienced a severe illness which required intensive medical care.
It has several presentations and may progress to severe illness.
He was reported to have fallen ill on 26 January and was diagnosed with a severe illness on 31 January.
"Flu is serious, causing severe illness and deaths in winter.
For patients with severe illness, they are worse than acute.
Unfortunately due to severe illness he could not use it.
During severe illness, heart rate variability is impaired.
TUCHMAN--Judith, died November 3, 2004, after a valiant attempt to live with a severe illness.
His composing career was abruptly terminated by a severe illness in 2005.
Many have seen severe illness in their families, and want to protect their children from suffering.
Spufford believes he became a book addict because of the severe illness of his younger sister.
Perhaps the cytomegalovirus had mutated to cause a more severe illness.
