Regularity and stability of neural impulse propagation in Alzheimer’s using an adapted Fitzhugh–Nagumo model

Abstract

This study presents an analytical framework for modeling the propagation of electrical impulses in a human brain affected by Alzheimer’s disease through an adapted FitzHugh–Nagumo model. The model incorporates the effects of amyloid plaques and neurofibrillary tangles on neural activity and connectivity. We include additional terms to account for disease-related effects and to provide a comprehensive approach to understanding the disruptions caused by Alzheimer’s disease. A priori estimates establish the boundedness of solutions, ensuring stability and regularity. The uniqueness of solutions is proven, indicating consistent results under identical initial conditions. Stability criteria is derived from linearizing the model around steady-state solutions. An exploration of specific parameters demonstrates the system’s stability for certain wave numbers, of relevance for maintaining proper neural communication.