Hi John, demodex is found on all humans, but only some individuals have a reaction to demodex. Therefore, it's reasonable to conclude: (1) the problem for afflicted people is an allergic reaction to demodex; (2) the allergic reaction is most likely the decaying body parts of demodex, as they have total life span of about 23-24 days,
and do not have an excretory opening during life; and, (3) Soolantra is an insecticide (or miticide, or acaracide), designed to suppress or eradicate demodex, an arachnid.
Accordingly, the most rational conclusion from the numerous Soolantra-success stories is that demodex induced or worsened rosacea in people who have a allergic reaction to demodex.
Here's a 2015 medical article on the subject of demodectic rosacea:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3884930/
However, medical science doesn't have a full explanation for allergic reactions -- as a result they tend to be ignored.
The connection to gut-level allergies is only that the immune system has a sort of "budget" to handle allergic reactions -- if a person has a gut-type allergy, then controlling the gut-type allergy will allow the immune system to exert more effective control other allergic reactions, such as demodectic rosacea or demodectic blepharitis.