Symbolism, Imagery, Allegory
It may be pretty simple symbol, but Machiavelli mentions tuberculosis twice, so it's worth noting. Actually, any kind of slow disease could work, so pick your poison.
If you think of the state as a body, then political trouble is just like tuberculosis—or, say, cancer. If you catch it early, it's not so hard to deal with, but if you miss it, "by the time it's big enough for everyone to see it will be too late to do anything about it" (3.9). The trouble is, it's really hard to catch diseases before there are a lot of symptoms, and when there are a lot of symptoms, it's often too late. So future rulers, keep an eye out—and remember to get your checkups.