Your problem discribed might be caused by funghi that have infected your papayas leaves. There are some of such infections described for Carica papaya, which is the botanical name of the plant. It would have been helpful to have a picture of an infected leave, to have a closer look at. According to your description, the funghus probably might be Corynespora cassiicola, being responsible for a desease called “Leaf-Blight“. This disease causes severe damage to leaves. First, it appears as small, discoloured lesions on the leaves which are irregularly scattered. These spots become irregular in shape, they increase in size and, finally, appear brown to grey in colour. A light yellow zone surrounds the spots. In a later stadium, several lesions coalesce and will cover large areas of the leaf. If the infection develops to be severe, the whole leaf dies. That may lead to a considerable reduction in the yield and may cause the death of the tree, after years.
If in fact it were Leaf-Blight, it can be controlled by spraying, starting form the early appearance of the disease symptoms. If available at your home, you could take the fungicide Dithane M-45 (0.2%) for spraying.
In general: Make sure that your papaya tree grows in a sunny to half shadowed place, with gently moving air as that dries the leaves when wet. So the funghi cannot spread over to the other leaves that easily. If you have planted the young trees at the same place as the cut off one has grown, take care that with spraying you cover the direct surrounding of your papaya tree to destroy the funghi in the close surrounding as well.
Photo: Private, Bryan Lau