Unraveling the link between beta cell dysfunction, insulin imbalance, and neurodegeneration in Alzheimer's disease

The onset and progression of Alzheimer's disease (AD) have long been strongly associated with obesity and diabetes caused by hyperglycemia, which leads to beta-cell dysfunction and insulin imbalance. This imbalance promotes the release of cytokines and activation of microglia, which play a crucial role in the production of amyloid-beta and neurofibrillary tangles. In this context, we formulate a delayed reaction-diffusion model of obesity induced AD to examine the dynamical behavior of the above biological hypothesis. We investigate the existence and uniqueness of solutions, stability of equilibria (local and global), sensitivity analysis as well as the occurrence of Hopf bifurcation and Turing instability. The findings highlight the importance of insulin diffusion rate, insulin secretion delay, glucose, and beta cell in developing AD and its effective control strategies. Spatiotemporal dynamics such as patchy patterns exhibit how A_β accumulates and spreads in the brain. A higher growth rate of beta cell supports sufficient insulin secretion, which can delay the progression of AD. In contrast, when beta cell growth is impaired, even a slight delay in secretion can accelerate disease progression. This study reveals that maintaining high-calorie food to support sufficient growth of beta cell and insulin for a long-term healthy lifestyle along with targeted anti-amyloid approaches can remarkably delay Alzheimer's progression.