Answer: I wish I could diagnose or identify the problem, but Papaya plants are attacked by a number of insect pests including:
The papaya fruit fly (Toxotrypana curvicauda), which lays eggs through the papaya fruit peel into the fruit cavity where the larvae feed and eventually emerge from the ruined fruit. This fly is commonly mistaken for a wasp due to its long abdomen and yellow and black markings. Fruit infested with papaya fruit fly may show yellow areas and may drop from the tree prematurely. The easiest control for this pest is to place a paper bag over individual fruit when they are small and leave the bag on until harvest.
The papaya webworm (Homolapalpia dalera) is mainly a pest of the developing fruit peel and papaya stem and is usually found in, on, or near the stem amongst the flowers and fruit. Control includes hand removal and hosing off the plant with a strong stream of water from a garden hose.
The papaya whitefly (Trialeuroides variabilis) is generally only a pest of the leaves causing, leaves to drop and reducing fruit production. Control includes removing infested leaves and applying appropriate pest control products.
The two-spotted mite (Tetranychus urticae) is a major pest of papaya leaves and may cause defoliation and early leaf drop. Symptoms include a browning of the leaf surfact and eventually upper leaf surfaces and skeletonizing of the leaf. For current control measures please contact your local County Extension Agent.
I'm afraid I don't know what type of pest might be attacking your bittermelon leaves. Not all pesticides are safe to use on all plants and not all will control all insects so identification is really important. If you can capture a few and take them into your local garden center, perhaps someone there can identify it for you and suggest a control option.
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