In everyday English, you can use “the” before the word "measles". However, we usually drop the article in formal contexts.
How do I know if I have the measles?
Can I get the measles if I've been previously vaccinated?
In professional or more formal situations, however, we usually drop the article before "measles".
Getting vaccinated is the best way to prevent measles.
Your doctor can diagnose measles by doing a blood test.
Because this noun is uncountable, you cannot use the indefinite article “a” in front of it.
Does he have the measles?
Does he have a measles?
And we never add an article or another determiner (the, this, etc.) when using "measles" in a general sense.
Measles is commonly a childhood disease, but it can affect individuals of any age.
The word "measles" can also function as an adjective. In such a situation, use the article a/an or another determiner (this, that, many, my, your, etc.) according to the usual rules.
She got a measles vaccine last year.