About. Autosomal recessive diseases in genetics
You are talking about an extremely simple system of inheritence that is a single bi-allelic locus with simple dominance relationships. You are talking about a autosomal recessive disease. In other words, let a and A be the two alleles, where A is dominant of a. By definition of your model, the individual expressing the disease is the individual carrying both a alleles (a aa individual). Anyone carrying the dominant allele would not express the disease (by definition of the term dominance and because you define a model where a and not A is causing the disease).

In short aa express the disease, while aA, Aa and AA individuals don't express the disease. aA and Aa are carrying the allele causing the disease though and might have kids expressing the disease if they mate with an individual that carries at least one allele a.