A rapid sickness is an illness or a disease.

This is a jukugo word that uses on'yomi readings, but you haven't seen the へい reading for 病 yet. In fact, this is pretty much the only word it appears in, and on top of that it gets rendaku'd. So here's a mnemonic to help you out:

If you don't treat an illness right away, you might pay (ぺい) with your life. And if you don't die, you'll still have to pay a lot for doctor and hospital fees. Yuck.