Soluble dimeric prion protein (PrP-Fc(2)) binds to the disease-associated prion protein PrP(Sc), and inhibits prion replication when expressed in transgenic mice. Prion inhibition is effective even if PrP-Fc(2) is expressed at low levels, suggesting that its affinity for PrP(Sc) is higher than that of monomeric PrP(C). Here, we model prion accumulation as an exponential replication cycle of prion elongation and breakage. The exponential growth rate corresponding to this cycle is reflected in the incubation period of the disease. We use a mathematical model to calculate the exponential growth rate, and fit the model to in vivo data on prion incubation times corresponding to different levels of PrP(C) and PrP-Fc(2). We find an excellent fit of the model to the data. Surprisingly, targeting of PrP(Sc) can be effective at concentrations of PrP-Fc(2) lower than that of PrP(C), even if PrP-Fc(2) and PrP(C) have the same affinity for PrP(Sc). The best fit of our model to data predicts that the replicative prion consists of PrP(Sc) oligomers with a mean size of four to 15 units.