@terren, are you asking whether there is a significant difference between your infected and non-infected groups?
Without knowing specifically what your results are, it’s impossible to give you a definitive answer, but I’m confident you can figure it out.
First, though, a question for you to answer:
Do the results of your alpha diversity commands have anything to do with the between-group difference you’re trying to quantify? What are alpha and beta diversity?
This post has already done a rather comprehensive job of answering your questions about interpreting beta-diversity, and seems to answer the question I think you’re asking.
In case it helps, you can think about Emperor/PCoA plots (like most data visualization tools) as useful tools for visually identifying trends in your data. Quantitative analysis, on the other hand, is necessary for determining whether the differences you’re seeing are statistically significant. Pictures make it easy to figure out what’s going on, but the numbers allow you to turn those insights into concrete findings.