In everyday English, you can use “the” before "mumps". However, we usually drop the article in formal contexts.

In everyday English or informal situations, we can use the definite article “the” before the term mumps.

Have you ever had the mumps?

We do not generally use articles with names of diseases or illnesses (conjunctivitis, asthma, cancer, etc.), but you can use the article “the” before some traditional names of diseases, such as the mumps, the flu, the chickenpox, or the measles.

She had the mumps in 2015.

However, in formal situations or professional contexts, we usually drop the article.

Vaccination is the best way to prevent mumps as well as mumps complications.

Mumps is a disease typically caught by children.

Being an uncountable noun, you cannot use the article “a” before mumps.

Does she have the mumps?

Does she have a mumps?

And omit the article to use this term in a general sense

Mumps is a viral disease caused by the mumps virus.

The word "mumps" can also function as an adjective. In this situation, use an article or another determiner according to the conventional rules.

A mumps outbreak is defined as three or more cases linked by place and time.