Answer: Based on your description it does sound like the tomatoes have early blight. Although there is a possibility the plants would continue to survive, the fruit quality and quantity will probably be poor and you will risk infecting more of your plants. Unfortunately the best thing to do in my experience is remove and destroy the infected plants.
Early blight is a fungus and it spreads very easily to both tomatoes and potatoes. Since the fungus will survive on infected leaves, stems, and in the soil as well as in the tomato seeds (and infected potato tubers) it is very important to clean up every bit of plant debris you can find.
In the future, you should also follow a careful three or four year crop rotation schedule to try to mimize the chances for a reoccurence. I'm sorry about your tomatoes.
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