Akito was going to die because he bared the core of the curse, but aside from that his death wasn't specified, only that he would eventually pass away at a fairly young age. Whether or not the curse made him sickly to begin with is also unknown.
I'm not sure what will happen to the Sohma's when Akito dies- since he is their god AND head of an entire family that branches out much more than the cursed Sohma's. I'm not sure if this happened to the other gods in the past (since Akito said it wasn't his decision- not sure if something happened or it was just his birth right.) If it happened to the gods before, then that means the Sohma curse will continue on the same. But none of it was revealed.
The anime's ending is much different from the manga, and the anime didn't explain very much of the ending. Hopefully this helped somehow, for the most part I'm just speculating.
