Stability Analysis of Mathematical Model including Pathogen-Specific Immune System Response with Fractional-Order Differential Equations
Author
Source
Computational and Mathematical Methods in Medicine
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-12-04
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
In this study, the mathematical model examined the dynamics between pathogen and specific immune system cells (memory T cells) for diseases such as chronic infection and cancer in which nonspecific immune system cells are inadequate to destroy the pathogen and has been suggested by using a system of the fractional-order differential equation with multi-orders.
Qualitative analysis of the proposed model reveals the equilibrium points giving important ideas about the proliferation of the pathogen and memory T cells.
According to the results of this analysis, the possible scenarios are as follows: the absence of both pathogen and memory T cells, only the existence of pathogen, and the existence of both pathogen and memory T cells.
The qualitative analysis of the proposed model has expressed the persistent situations of the disease where the memory T cells either do not be able to respond to the pathogen or continue to exist with the disease-causing pathogen in the host.
Results of this analysis are supported by numerical simulations.
In the simulations, the time-dependent size of the tumor population under the pressure of the memory T cells was tried to be estimated.
American Psychological Association (APA)
Daşbaşı, Bahatdin. 2018. Stability Analysis of Mathematical Model including Pathogen-Specific Immune System Response with Fractional-Order Differential Equations. Computational and Mathematical Methods in Medicine،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1132179
Modern Language Association (MLA)
Daşbaşı, Bahatdin. Stability Analysis of Mathematical Model including Pathogen-Specific Immune System Response with Fractional-Order Differential Equations. Computational and Mathematical Methods in Medicine No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1132179
American Medical Association (AMA)
Daşbaşı, Bahatdin. Stability Analysis of Mathematical Model including Pathogen-Specific Immune System Response with Fractional-Order Differential Equations. Computational and Mathematical Methods in Medicine. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1132179
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1132179