I'm having the same problem with my cucumbers but I don't want to spray with anything because of my two lovely Praying Mantises who are permanent residents of these vines.

I recommend the yellow sticky traps, but it maybe too late for your level of infestation, especially eggplant.

FWIW: probably not an immediate solution to your problem, but this works quite well for me. "the basic premise of my pest control program is: "everybody"s somebody"s lunch. I've got a variety of native plants throughout the yard (attracts birds) and I don't spray (allows beneficial insects to thrive). The ladybugs, lizards, birds and spiders have been reliable pest control, even during the whitefly infestation of a few years ago. I did have a mess develop on the bottom side of the banana leaves, which I sprayed twice with diluted insecticidal soap. Best luck.

Jim: Will yellow sticky traps catch ladybugs or other predatory insects?

sonni1: What dilution do you use with insecticidal soap? Will baby shampoo work just as well?

i catch very few predatory insects. I do not think the predatory insects in No CA are attracted to yellow. I think the one lady bug I have caught in 10 years may have been blown to the sticky paper or was trying to eat a aphid. I released the LB, but it did not fly away, maybe the LB lost a leg or two. Meat bees are probably strong enough to get away.

I'm not sure how you can have white flies because all of them are on my green beans. I think I inhaled about a pound of them when harvesting this weekend.

I'm glad that you have some green beans to harvest.

Actually they haven't seemed to be affecting the bean plants much if any so far. I've harvested 18 lbs. over the last 10 days and need to harvest again in the next couple days. I have 4 - 10' rows of 3 varieties planted which is way too many!

Re: insecticidal soap dilution. I'm not one to do any exact measuring in the garden. If I recall, there are directions for application on the bottle. It's fairly potent straight, so I would guess a 50/50 would still be effective. For the soap to kill the insect, it needs to be in contact with it for a bit of time, the spraying removes the bugs from the plant,but I doubt that it kills them.