Stationary distribution of a stochastic Alzheimer's disease model.

In this paper, based on the pathogenesis of Alzheimer's disease, we investigate a stochastic mathematical model, focusing on the dynamics of β‐amyloid (Aβ) plaques, Aβ oligomers, PrPC proteins, and the Aβ‐x‐PrPC complex. Within the framework of the Lyapunov method, we first show existence and uniqueness of global positive solution of the model and then establish the sufficient conditions for existence of an ergodic stationary distribution of the positive solution. Ultimately, numerical examples are presented to illustrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]