Hi Katharine, I might have a perfect solution to your problem.

1. You can use this Unofficial Medium API (http://hub.mediumapi.com) to scan your publication's articles over a period of time.

2. Then fetch all the responses from each article and sort them by individual readers.

3. So you can get the count of the responses a reader left on your publication articles.

And if you're a python programmer, then it's even easier to implement with "medium-api" python package.

Let me know if your need any help with that.

And full disclaimer: I'm the creator of that Unofficial Medium API