We present the development of a two-stage PrNi5 continuous demagnetization refrigerator at the Institut Nel/CNRS and numerical simulations of its performance. The thermal model used in the simulations is discussed in detail including the likely sources of heating. We demonstrate the effects of the critical thermal links including superconducting heat switches as well as the heat conductivity of the PrNi5, accounting for the dependence of cooling power on the PrNi5 rod diameter. Our simulations show that if care is taken to minimize the thermal resistance between the nuclear stages, a sample temperature of 1 mK can be maintained under a 20-nW heat load.