Weak solution and global qualitative behaviour of a prion proliferation model in the presence of chaperone

Abstract

In this article, a prion proliferation system in the presence of a chaperone, which involves two ODEs and an integro-partial differential equation, is studied. The existence of weak solution results obtained in Laurençot and Walker (J. Evol. Equ. 7:241–264, 2007) is extended by incorporating chaperone. Further, we study the uniqueness of solution under the sufficient conditions proposed in Laurençot and Walker (J. Evol. Equ. 7:241–264, 2007). In addition, the qualitative global results of disease and disease-free equilibrium points are proved analytically. The effect of the chaperone on prion population is also presented numerically.