Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31181
Stability Analysis of Two-delay Differential Equation for Parkinson's Disease Models with Positive Feedback

Authors: M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Simulation, Stability, parkinson's disease, two delay differential equation

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 128

References:


[1] Yoshio Tsuboi, Environmental-Genetic Interactions in the Pathogenesis of Parkinson's Disease, Exp Neurobiol. 2012 Sep;21(3):123-128
[2] G. Austin and Chen TSAT, A Physiological Basis and Development of a Model for Parkinsonian Tremor, Ist Int. Symp. Stereoencephalotomy, Philadelphia 1961. Confin. neurol, 22: 248-258 (1962)
[3] Claudia Lainscsek, Luis Schettino, Peter Rowat Elke van Erp, David Song and Howard Poizner V.In, et al. (eds.), Applications of Nonlinear Dynamics,Understanding Complex Systems Springer. 2009.
[4] Hal Smith, An Introduction to Delay Differential Equations with Sciences Applications to the Life. Springer, New York, NY. DOI https://doi.org/10.1007/978-1-4419-7646-8
[5] E. Ahmed, A Delay Model Motivated by Parkinson Disease. JRL J Sci Technol. 2019; vol1-iss1: jst1002
[6] Agiza, H. N., M. A. Sohaly, and M. A. Elfouly. "Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease." International Journal of Mathematical and Computational Sciences 14.12 (2020): 159-163.
[7] Alain L Fymat. “Neurological Disorders and the Blood Brain Barrier: 2. Parkinson and Other Movement Disorders”. Current, Opinions in Neurological Science 2.1 (2018): 362-383.