Firstly, I am not a teacher.
However, I am pretty sure about the use of only in the subjected sentence, as I understand it from the medical point of view. It means that the disease is contagious (i.e. transmissible, possesing capacity of infecting somebody) in early stages only.
The word only refers to the early stages, not to the word contagious.
The collocation "only contagious" has no sense, as there is nothing more (or less) than contagious. The disease can be contagious or not, nothing else.