As far as I know there is no cure. I think this is a type of fungus and can be present in the soil or on plant material left on the soil surface. The plant should be removed as well as some of the surrounding soil. Sorry this is probably not what you wanted to hear.

On the issue of fusarium wilt.
Once your plant has it, there is nothing you can do.
It's a done deal. That plant is infected and will only continue to die a slow and painfull death.
But there is good news on the fighting of this powerful disease. HEAT! and alot of it.
First,you want to clear off all of your growing area of any of the infected plant material including roots. Any large weeds and their roots have to go too.
Burn or discard these plants in trash NOT IN THE COMPOST PILE!
Next, in the hot summer months spread thick clear plastic over the growing area that is infected and use steaks or bricks,logs etc. to hold down the plastic.
Next leave there for at least 30 days, 60 is better.
The heat will kill the fugus and just about everything else including the beneficial organic life forms.
But don't dispair.
Plant a cover crop like clover or buckwheat and plow/till it under in fall or following spring.
The clover and or buckwheat will regenerate the soil and reintroduce new healthy organic life back into the soil.
To minimize the recurrance of the disease, avoid planting more than 2 seasons back to back of the tomato family of plants. In other words, rotate crops.
And choose only plants labled (V-F) on the tags.
The V and F stand for Verticlum and Fusarium resistant.
Thanks, hope this helps, it fixed my garden.