The most common and most likely answer to this crossword clue is the 9 letter word OUTBREAKS
I've seen this crossword clue in Financial Times
O
U
T
B
R
E
A
K
S
More clues leading to the result OUTBREAKS
Buddy explains!

The straight part
We know that "Occurrences of disease" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case occurrences of disease = outbreaks.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does OUTBREAKS mean?
OUTBREAKS noun- An eruption; the sudden appearance of a rash, disease, etc.
- An outburst or sudden eruption, especially of violence and mischief.
- A sudden increase.
- A geological layer that breaks out.
- To burst out.
- To break forth.