Despite experimental evidence that scrapie is an infectious disease of sheep, variations of the occurrence of the natural disease suggest an influence of host genetic factors. It has been established that the genetic polymorphism of the prion protein (PrP) gene is correlated to the incidence of scrapie and to the survival time: five polymorphisms have been described by variations at amino-acid codons 136, 154 and 171. In this paper we study the effect on scrapie susceptibility of the pairing of the five allelic variants known to exist: we show that scrapie susceptibility is given by the produce of the elementary allelic factors. This first well-documented evidence of a multiplicative property of genetic risk factors could give hints on the underlying mechanisms of prion-induced neurodegenerative diseases.