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, PrP^C proteins, and the Aβ‐x‐PrP^C 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.

中文翻译：

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随机阿尔茨海默氏病模型的平稳分布

在本文中，基于阿尔茨海默氏病的发病机理，我们研究一个随机数学模型，专注于β淀粉样蛋白的动力学（Aβ）斑块，Aβ寡聚体，PrP的^Ç蛋白和Aβ-X-的PrP ^Ç复杂。在Lyapunov方法的框架内，我们首先显示模型的整体正解的存在性和唯一性，然后为正解的遍历平稳分布的存在建立充分条件。最后，通过数值例子说明了理论结果的有效性。