Hi, I think it would be bacterium, if you don't plan on burning the plant to stop the spread. I would try mixing Epsom Salt in water. [ small amount 1/4 tea spoon in a pint.] The area where the plant is should not be in overly damp conditions. Spray the leaves with the mixture when not in direct sun there should be air movement by fan if necessary. you can do this often two to four tines a day. The plants will ingest the Magnesium quickly. I did this last year with good results.
Try this on one plant first. and please describe the results. Thanks Richard
If your pepper plants are in damp conditions with little or no air movement it is perfect conditions for bacterium growth. Have a good day.
You can remove a few of the worst leaves.