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Good for you to be able to create such shareable content! I have one post I wrote that occasionally gets a boost of virality and I'll tell you what I did (but I am by no means an expert on how to make the best use of viral traffic.) -I put links in that article to other interesting/related articles on my site. -I encourage people to share or link to this article if they have found it helpful.  (If you're not already doing it, you may consider adding a block of code to show people how to link to the article, for those who are not html savvy.) Another thing you can do is use this article to look for linkbuilding opportunities.  If that many people are willing to share and read your stuff then you should have people who want to link to it.  Depending on the content you can look for other websites that are linking to this kind of stuff and then suggest your site as a resource to link to.  Similarly, you can do broken link building.  Find sites that link to your kind of content, then search for broken links (I use the chrome check-my-links extension).  Then, you can send them an email saying, "Hey, I found some broken links on your site.  I was wondering who I could report them to...and by the way, you may find this article of mine worth linking to.) Care to share your tips on how you make an article attract so much attention?

Ryan is correct. You should not worry about it - if worry about it then you will naturally try to alter the ratio to something that is NOT natural. My guess is that there is a flag in googles algorithm when it see's a ratio of dofollow to nofollow that is well above the norm. SEO's concentrate on dofollow links, therefore it is an indication of possible manipulative tactics if you see a very high ratio (one that would not occur naturally).