Answer: Your plants could be suffering from either early or late blight, which are caused by different fungi. Early Blight is caused by the Alternaria fungus. It overwinters on infected plant material, even seeds, so it's hard to completely remove the spore reservoir from the garden by cleaning up all the vines and fruit. Early Blight works slowly, whereas Late Blight (caused by the Phytophthora fungus) may kill plants within a week. The fungus is always growing somewhere and releasing spores into the air, which moves on wind currents. There's no cure for the disease.
Try to keep your plants healthy so they'll be in top condition to resist disease. Stake or cage them, and keep the lowest leaves from coming in direct contact with the ground. There are other disease and pest problems that may be affecting your crop, such as Verticillium wilt and Fusarium wilt.
When choosing tomato varieties, look for the words "disease-resistant" or the letters V (verticillium), F (fusarium), N (nematodes), T (tobacco mosaic), and A (alternaria). As far as I know, there are no varieties resistant to the late blight fungus (Phytophthora).
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