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.
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.