Sorry, feeling a bit under the weather myself today, so the topic will be illness in the Christie canon, specifically flu.
The story goes that young Agatha ran out of books when she was home with the flu, and her mother indicated that if she'd completed all the books in the house that she'd best write her own. Of course, it's no small matter that one of her early links to the world of writing came from the flu.

So after that impetus from disease, it's not surprising that the flu crops up in a few stories. The first is "The Case of the Caretaker," where Doctor Haydock brings Miss Marple a puzzle to contemplate. She'd been ill and not back to her usual self yet. The solution of the puzzle helps her spirits and her health.

In Sparkling Cyanide, it is Rosemary who "commits suicide" as a result of post-flu depression, and Iris who is the younger daughter. While it sounds like a flimsy excuse, apparently the idea has been around for over 130 years, which means the diagnosis was available at the time of the book. Of course, later it's proved that Rosemary did not commit suicide (given that this is Christie, I don't think that's a particular spoiler.)
Curran has very little to say about this book, so we can't fill in many of the details here, but it would be interesting to know if the idea of post-flu depression came from a friend who suffered from it or just her knowledge of medicine.
Again Miss Marple has been under the weather in A Caribbean Mystery, which finds her on an island recuperating. It's quite possible that she has had the flu.
Have I missed other examples of illness (specifically flu) in the Christie books?