Delaney said: "My wife and Henry's older brothers and I are devastated of course".
The Catastrophe on-screen character and author took to the web-based social networking stage to report that his child Henry has passed away.
Henry had suffered weight loss and constant vomiting, and it was after Henry's first birthday that they knew of his disease. He was savvy, clever, and naughty and we had such a significant number of great experiences together, especially after he'd moved home after fifteen months living in doctor's facilities.
He encouraged everyone to do an act of kindness by donating to Rainbow Trust and Noah's Ark, organizations which help families with kids who have terminal diseases. "His drive to live and to love and to connect was profound".
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Though left with "significant physical disabilities", Henry learned sign language and shuffled from place to place "on his handsome little bum".
You can read Delaney's full message below. He commended the nurses and doctors who aided his family.
"They are why I will endeavour to not go mad with grief". I don't want to miss out on their attractive lives. Henry was the youngest of three children Rob shares with his wife of 11 years, who he has yet to name publicly.
Calling the NHS nurses and staff who treated his son as heroes, he urged people to donate to United Kingdom charities for sick children in Henry's name. I took you and Henry to GOSH one day a year ago and it stuck with me what an absolute trooper of a boy he was.
The "Catastrophe" star thanked the "heroes" who had helped the family along the way and ended the statement by saying, "Thank you, attractive Henry, for spending as much time with us as you did".
While American, Delaney has mainly found success in the United Kingdom, in large part due to the hit TV series Catastrophe, the show he co-created alongside fellow co-star Sharon Horgan. "I am desperately sad right now, but I can say with authority that there is good in this world", he wrote. "We miss you so much", Delaney ended the post.