Stationary distribution of a stochastic Alzheimer's disease model |
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| Authors: | Jing Hu Qimin Zhang Anke Meyer-Baese Ming Ye |
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| Institution: | 1. School of Mathematics and Statistics, Ningxia University, Yinchuan, China;2. Department of Scientific Computing, Florida State University, Tallahassee, Florida, USA;3. Department of Scientific Computing, Florida State University, Tallahassee, Florida, USA
Department of Earth, Ocean, and Atmospheric Science, Florida State University, Tallahassee, Florida, USA |
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| Abstract: | 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. |
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| Keywords: | Alzheimer's disease ergodic stationary prion proteins stationary distribution stochastic model |
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