A mathematical model describing the evolution of a population dynamics problem in which, a genetically transmitted disease, Sickle-cell Anaemia, is prevalent is considered. The genotype or physiological structure of individuals divides such a population naturally into three genotypic groups, namely; normal (AA), carriers (AS) and sickle-cell suffers (SS). An a priori estimates of the solution is obtained as well as conditions under which such a solution is unique.