Document Type

Article

Source of Publication

Results in Physics

Publication Date

1-1-2021

Abstract

This paper is devoted to develop a new mathematical model for Alzheimer disease based on a system of fractional-order partial differential equations. The system of Alzheimer disease includes neurons, astrocytes, microglias and peripheral macrophages, as well as amyloid β aggregation and hyperphosphorylated tau proteins. We consider the Caputo fractional derivative definition to analyze the formulated system by simulating the effect of drugs that either failed or currently in clinical trials. To simulate the model, we use tight frame (framelet) systems generated using the unitaryand oblique extension principle. According to the simulation results, and based on using such new direction of fractional modeling, the progression of Alzheimer disease and its consequences will be slowing down. Which may give clinical insights on intervention measures against the disease and its effective therapies.

ISSN

2211-3797

Publisher

Elsevier B.V.

Volume

21

First Page

103809

Disciplines

Physical Sciences and Mathematics

Keywords

Alzheimer disease; Caputo's fractional derivative; Drug treatment; Mathematical modeling; Tight frames; Time fractional differential equation

Scopus ID

85099835016

Indexed in Scopus

yes

Open Access

yes

Open Access Type

Gold: This publication is openly available in an open access journal/series

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