Well, I study homeopathy and the answer is simple.

Unfortunately, many of the homeless are also mentally ill, and homeopathy (specifically, Hering's law of cure) teaches us that if you are very very sick on the mental plane, it is harder to get sick on the physical plane. Much harder to catch a cold or get any kind of infectious disease on the physical plane.

Study Hering's Law of cure and the law of suppression.