Prion dynamics with size dependency–strain phenomena

Models for the polymerization process involved in prion self-replication are well-established and studied [H. Engler, J. Pruss, and G.F. Webb, Analysis of a model for the dynamics of prions II, J. Math. Anal. Appl. 324 (2006), pp. 98–117; M.L. Greer, L. Pujo-Menjouet, and G.F. Webb, A mathematical analysis of the dynamics of prion proliferation, J. Theoret. Biol. 242 (2006), pp. 598–606; J. Pruss, L. Pujo-Menjouet, G.F. Webb, and R. Zacher, Analysis of a model for the dynamics of prions, Discrete Cont. Dyn. Sys. Ser. B 6(1) (2006), pp. 215–225] in the case where the dynamics coefficients do not depend on the size of polymers. However, several experimental studies indicate that the structure and size of the prion aggregates are determinant for their pathological effect. This motivated the analysis in Calvez et al. [Size distribution dependence of prion aggregates infectivity, Math Biosci. 217 (2009), pp. 88–99] where the authors take into account size-dependent replicative properties of prion aggregates. W...