What is the Johnsy's illeness? What can cure her, the medicine or the willingness to live?

Johnsy was suffering from pneumonia and was not recovering. She assumed that she would die with the fall of the last leaf of the creeper she could see through the window.

No medicine in the world can ever cure a person who believes in and develops a pessimistic outlook towards life. It is only the willingness to live that can cure a person in such a situation.