Bifurcation Analysis and Finite-Time Contraction Stability of an Alzheimer Disease Model

Abstract

In this paper, considering reaction–diffusion, delay and random disturbances, two classes of mathematical models associated with Alzheimer’s disease (AD) are developed. For the deterministic AD model, the stability of the unique positive equilibrium and the Hopf bifurcation are analyzed. On the other hand, focusing on the influence of uncertain factors in the environment on AD, we investigate the finite-time contractive stability (FTCS) for the stochastic AD model modulated by Markov switching process. The basic method used to formulate the FTCS of the system is the comparison method. Several illustrative examples are considered to demonstrate and verify the effectiveness of the obtained theoretical results.