This is a hard problem to diagnose because it could be something as simple as a potassium deficiency or a fungal wilt; which could be a bacterial wilt, fusarium wilt or verticillium wilt, or a bacterial canker; from what I can find about brown/black wilted leaves. It does not look like curly top which is spread by leaf hoppers. If this is the case, remove affected parts and use a row cover to protect the plants. As well as using a compost around the plants. There are other controls to deal with leaf hoppers.
If it is a potassium deficiency, kelp meal, granite dust, greensand and sparingly wood ashes added to the soil might reverse the problem. Epsoma products are the best to use(Amazon.com or sometimes Lowe's carries this product)
I refer to the book I have in my library and recommend it to you as well; perhaps you can find it at a local library:
The Organic Gardener's Handbook of Natural Pest and Disease Control by Fern M. Bradley, Barbara Ellis, Deborah Martin: states on page 208 under Tomatoes that: symptoms:
" leaves with brown edges. Cause: Bacterial canker. Lower leaves wilt and curl up; stems develop light colored streaks and are brown and mealy inside. Destroy infected plants. To prevent problems, avoid wounding plants; don't work amid wet plants."
(I know this entry does not help at all...)
Further, on page 324-325 on the bacterial wilt, fusarium or verticillium: the entries read:
for fusarium "Wilt fungi cause leaves to yellow and leaf stems to droop, giving plants a wilted appearance. The yellow leaf patches turn brown and may spread to cover whole leaves. Leaves often fall early, and the plants will die. Symptoms usually first appear on the lower or outer parts of plants; or on one side of a plant. Common hosts include tomatoes, peas, peppers, melons, dahlias and mimosa trees. Fusarium wilt thrives in warmer areas. Verticillium wilt is more common in cool weather in temperate area of the country.
With Fusarium wilt, plant resistant cultivars. Crop rotation is of limited value because it can survive in the soil a number of years even in the absence of a susceptible plant. Remove and destroy infected plants. Soil solarization may reduce the incidence.
There is also, no remedy or cure for V. wilt. the mose effective preventive is the use of wilt resistant cultivars.
Adding compost to soil may help by boosting populations of beneficial fungi.
I know this is all complicated and there is no easy answer. I hope that another DG can better diagnose and give you other measures. Good luck!
