Homers or all pigeons in general are subject to the same illness. Whether it may be an infection from a parasite or just any usual common illness, it can be treated in the most effective ways early in the process.
According to my experience, my birds have not been infected. What I do see in my birds are pigeon lice and mites. Those little critters can be taken care of by using pet dust from any Wal-Mart or feed store located in your area. Once you have the product, you can dust the birds on the inside of its wings, back, and chest avoiding the eyes and beak. You can also dust the area in which the pigeon is confined in also for extra protection.
Vitamin supplements such as Vitamins and Electrolytes powder can also be used in their drinking water or as a food supplement.