| Abstract: |
| Evidence suggests that obesity, diabetes, and aging notably increase susceptibility to dementia related conditions such as Alzheimers disease. This work explores the correlations between obesity, diabetes, and this disease. It introduces a reaction diffusion model encompassing variables like glucose dynamics, insulin levels, microglia, cytokines, plaques, neurofibrillary tangles, and cognitive decline. The system proposed is an example of a partly dissipative system, as there is a lack of smoothing in several of the state equations. Despite this challenge, we explore the long time behavior of this system, via showing the existence of a global attractor. Several control strategies for the disease are also proposed. |
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