Number count on Messages App

Since updating my Mac Mini on Sept. 18th and 19th to Safari 12, and updating Pages, Numbers and Keynote, the Messages icon on my dock now always shows a number count for unread texts, but there are none when I open it. I know it used to happen awhile back, but that was on my iPhone, not my computer. This is not happening on my iPhone this time, nor on my MacBook Air. I've tried a few things to clear the number count, closing/reopening Messages, rebooting the Mini, and ran Disk Utility. No joy yet. Not sure what to try next, or if this is a bug that I should report to Apple.