The day after we got back from our cruise I got what I guess was the famous norovirus that is popular on ships. Which I know it is just food poisoning and that can happen anywhere.
I think you are going to find many people who know someone who has gotten sick. I wouldn't keep let that keep you from going on a DCL cruise unless you have an auto-immune disorder or some other condition that places you at high risk.
But we still go knowing we will probably get something from a simple cold to flu like symptoms.Also do not touch the rail of the stairs, let someone else touch the buttons on the elevators or have a handkerchief to do so. Train yourself not to touch your face. And clean your cutlery before dinner.Some things that can help are to take Vitamin C daily, wipe down all handles/switches/remotes/phone/buttons, etc. in your cabin upon arrival, washing hands before eating and upon every arrival back to your cabin, and keeping Zicam (high-potency zinc) tablets with you, to take the moment you start to sense any type of cold coming on.
That might sound like a lot, but it's really no big deal to do & becomes habit once you get used to it. As an elementary teacher, I'm used to taking precautions to minimize the spread of illness. It helps.