An Improved Alzheimer-Like Disease Computational Model via Delayed
Hopfield Network with Lurie Control System for Healing
Abstract
Alzheimer’s disease (AD) is a degenerative neurological condition that
impacts millions of individuals across the globe and remains without a
healing. In the search for new possibilities of treatments for this
terrible disease, this work presents the improved Alzheimer-like
disease (IALD) model and connects it to a new control technique that
establishes computationally modeled memory healing for a condition
similar to AD. The modeling proceeds from recent etiological and
pathogenetic hypotheses of AD related to amyloid precursor protein
(APP). For the IALD model, a continuous Hopfield neural network (HNN)
with delay is used. In the control, techniques from the area of robust
control are used, which is based on new discoveries in Lurie control
systems. In addition, this paper reviews the development of the
Alzheimer-Like Disease (ALD) model, as well as, the relationship of
Hopfield’s network with Lurie system. Simulations are executed to
validate the model and to show the efficacy of applying a new theorem
from Lurie’s problem. With the results presented, this work puts to good
use, from the \textit{in silico} IALD model, the
possibility of developing microcontrollers for future
\textit{in vivo} experiments using a control system
capable of mitigating the effect of memory loss arising from AD.