How to notify Web Browser clients of DB changes

We have a MYSQL database, with quite a few tables that are being constantly updated by many users.
We have rows of data that are presented to users through a web page.
Currently, the page data is refreshed every minute via AJAX. If someone makes a change on the web page, it is posted back to the server through AJAX. With the information being time critical, this is obviously not the best option, as we really need the information to update in near real-time.

What are the best options for performing this task?