He's dying of pneumonia.
Appendicitis nearly killed him.
She has cancer
(You will sometimes hear "the measles," "the mumps," but these, too, can go without articles.)
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Interested in Language
Do the following diseases require a definite article?
(the) Mumps, (the) measles, (the) hepatitis, (the) chicken pox.
Measles and mumps can go either way, with or without an article. Chicken pox sounds better without the article:
"I had chicken pox as a child."
"You can't come in the house unless you've already had chicken pox; the kids are all contagious right now."
Hepatitis never gets an article, although it is often expressed by specifying the strain of the disease:
"She caught Hepatitis C from sharing a dirty needle."
"My friend caught Hepatitis while working witht he Peace Corps in Sudan."