That looks like it might be early blight.

Here is a link that might be useful: Early blight

Looks much more like Septoria leaf spot (early blight produces spots with dark centers, not edges). Septoria is also encouraged by wet, warm weather.

It is extremely important that you rotate the location of your veggies each season, especially the solanceous ones (tomatoes, potatoes, peppers, eggplants, etc.), to limit the spread of the fungal diseases that can plague these plants. Also to practice very strict garden sanitation - clean everything up thoroughly at the end of the season. You can try an organic fungicide - copper sprays, potassium bicarbonate or Bacillus subtilis - to limit the foliar damage. Fruit is usually unaffected but excessive foliage damage can weaken the plant and limit flowering and production.

If you do choose to replant, pick another location. Do not replant with tomatoes in the same area for at least 3 years.

Here is the response I got from my local extension:

Your tomatoes (and most tomatoes on farms) have septoria leaf spot, a fungal disease that is a little more aggressive than early blight. Most fungal and bacterial diseases start on the lower leaves and work their way up the plant.

If you have the option to pull a few plants with this disease and plant some from a local greenhouse, that may protect the rest of the planting. If the spots are on too many plants to pull them all, then you can at least slow it down by removing lower leaves. Without a commercial fungicide, it may still spread.

Should the effected leaves be burned or will the fungus be destroyed in a hot compost pile?

Many places have burning bans in place so burning would not be an option for many people. Some people do object to the burning bans because they simply will not understand that the pollution they create by burning causes health problems for many people.
If you can get the temperatures of your compost pile high enough, long enough, to kill the disease spores you can compost the infected plants.