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Stationary distribution of a stochastic Alzheimer's disease model
Author(s) -
Hu Jing,
Zhang Qimin,
MeyerBaese Anke,
Ye Ming
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6642
Subject(s) - uniqueness , ergodic theory , mathematics , stationary distribution , distribution (mathematics) , lyapunov function , statistical physics , mathematical analysis , markov chain , statistics , physics , nonlinear system , quantum mechanics
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.