They can lay eggs if needed (this is usually the over-winter stage). If their host plant dies, they can grow wings and fly away to a new plant. These guys are very adaptable. If you catch them early before they are an entire colony you may be able to control them with a mild soapy water and gently wash them off the plants. Be sure not to let any get away, because in three days one aphid can become fifteen. You should rinse the plant off with water after using the soap as there is a chance the soap could burn the plant. Alternatively, there are several organic and non-organic sprays for aphids. Make sure they list peppers on the label and also that it is used for controlling aphids. Both of these practices may take a couple of treatments to get rid of the aphids completely. I have noticed that plants that are kept on the dry-side when watering tend to have fewer aphid problems, but don’t cut your watering back to the point that it harms the plant.