The child has signs of sickness, should be right
The child has symptoms of a disease should also be right
10-MAY-2018: Reported that "The child has symptoms of illness" should be an accepted answer.
Also reported that: "The child has symptoms of disease" should be accepted. (Currently says that "the" isn't needed)
An article is needed here. The child or a child. No way to report.
I reported twice: the corrected solution is unnatural.