Global dynamics for a model of amyloid fibril formation in pancreatic islet beta cells subjected to a therapy

Amyloid polypeptide (IAPP) fibril formation is the main cause of type II diabetes mellitus (T2DM) disease and cardiovascular disease (CVD). Therefore, implementing therapeutic interventions strategies to control IAPP fibril formation plays a crucial role in preventing and managing T2DM disease and CVD. For this purpose, in this paper, we make use of a mathematical model to investigate the effects of drug therapy on the dynamics of amyloid fibril formation (or amyloid plaques). The model is a hybrid system of differential equations consisting of ODEs and (hyperbolic) PDE. The (global) stability analysis is established through the construction of suitable Lyapunov functionals and application of Lasalle's invariance principle. Moreover, stability of the disease steady state is fully determined by a threshold condition, which is based on the total population of IAPP polymers.