Thermo-kinetic model for Prion diseases

A mean field theory of the auto catalytic Prions conversion reaction is developed under a conservation law for Prions density. These reactions take place in the brain where a normally folded Prion protein (Pr Pc) is converted into a misfolded, more stable, form (Pr PSc). The results reproduce most of the known facts observed in Prion diseases such as: very long incubation time, rapid death after the first symptoms manifestation, dependence of the incubation and death times on the concentration of the initial contamination dose and the existence of a minimum contamination dose for the detection of the disease. Results of computing simulations are also presented.