Fractional order modeling and analysis of dynamics of stem cell differentiation in complex network

Ram Singh; Attiq U. Rehman; Mehedi Masud; Hesham A. Alhumyani; Shubham Mahajan; Amit K. Pandit; Praveen Agarwal

doi:10.3934/math.2022289

Fractional order modeling and analysis of dynamics of stem cell differentiation in complex network

Ram Singh
, Attiq U. Rehman
, Mehedi Masud
, Hesham A. Alhumyani
, Shubham Mahajan
, Amit K. Pandit
, Praveen Agarwal

Baba Ghulam Shah Badshah University
Taif University
Shri Mata Vaishno Devi University
International College of Engineering

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this study, a mathematical model for the differentiation of stem cells is proposed to understand the dynamics of cell differentiation in a complex network. For this, myeloid cells, which are differentiated from stem cells, are introduced in this study. We introduce the threshold quantity R0 to understand the population dynamics of stem cells. The local stability analysis of three equilibria, namely (i) free equilibrium points, (ii) absence of stem and progenitor cells, and (iii) endemic equilibrium points are investigated in this study. The model is first formulated in nonfractional order and after that converted into a fractional sense by utilizing the Atangana-Baleanu derivative in Caputo (ABC) sense in the form of a non-singular kernel. The model is solved by using numerical techniques. It is seen that the myeloid cell population significantly affects the stem cell population.

Original language	English
Pages (from-to)	5175-5198
Number of pages	24
Journal	AIMS Mathematics
Volume	7
Issue number	4
DOIs	https://doi.org/10.3934/math.2022289
State	Published - 2022
Externally published	Yes

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This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Cell production system
Non-singular kernel
Stability analysis
Stem cell

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10.3934/math.2022289

Cite this

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title = "Fractional order modeling and analysis of dynamics of stem cell differentiation in complex network",

abstract = "In this study, a mathematical model for the differentiation of stem cells is proposed to understand the dynamics of cell differentiation in a complex network. For this, myeloid cells, which are differentiated from stem cells, are introduced in this study. We introduce the threshold quantity R0 to understand the population dynamics of stem cells. The local stability analysis of three equilibria, namely (i) free equilibrium points, (ii) absence of stem and progenitor cells, and (iii) endemic equilibrium points are investigated in this study. The model is first formulated in nonfractional order and after that converted into a fractional sense by utilizing the Atangana-Baleanu derivative in Caputo (ABC) sense in the form of a non-singular kernel. The model is solved by using numerical techniques. It is seen that the myeloid cell population significantly affects the stem cell population.",

keywords = "Cell production system, Non-singular kernel, Stability analysis, Stem cell",

author = "Ram Singh and Rehman, \{Attiq U.\} and Mehedi Masud and Alhumyani, \{Hesham A.\} and Shubham Mahajan and Pandit, \{Amit K.\} and Praveen Agarwal",

note = "Publisher Copyright: {\textcopyright} 2022 the Author(s), licensee AIMS Press.",

year = "2022",

doi = "10.3934/math.2022289",

language = "English",

volume = "7",

pages = "5175--5198",

journal = "AIMS Mathematics",

issn = "2473-6988",

publisher = "American Institute of Mathematical Sciences",

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TY - JOUR

T1 - Fractional order modeling and analysis of dynamics of stem cell differentiation in complex network

AU - Singh, Ram

AU - Rehman, Attiq U.

AU - Masud, Mehedi

AU - Alhumyani, Hesham A.

AU - Mahajan, Shubham

AU - Pandit, Amit K.

AU - Agarwal, Praveen

PY - 2022

Y1 - 2022

N2 - In this study, a mathematical model for the differentiation of stem cells is proposed to understand the dynamics of cell differentiation in a complex network. For this, myeloid cells, which are differentiated from stem cells, are introduced in this study. We introduce the threshold quantity R0 to understand the population dynamics of stem cells. The local stability analysis of three equilibria, namely (i) free equilibrium points, (ii) absence of stem and progenitor cells, and (iii) endemic equilibrium points are investigated in this study. The model is first formulated in nonfractional order and after that converted into a fractional sense by utilizing the Atangana-Baleanu derivative in Caputo (ABC) sense in the form of a non-singular kernel. The model is solved by using numerical techniques. It is seen that the myeloid cell population significantly affects the stem cell population.

AB - In this study, a mathematical model for the differentiation of stem cells is proposed to understand the dynamics of cell differentiation in a complex network. For this, myeloid cells, which are differentiated from stem cells, are introduced in this study. We introduce the threshold quantity R0 to understand the population dynamics of stem cells. The local stability analysis of three equilibria, namely (i) free equilibrium points, (ii) absence of stem and progenitor cells, and (iii) endemic equilibrium points are investigated in this study. The model is first formulated in nonfractional order and after that converted into a fractional sense by utilizing the Atangana-Baleanu derivative in Caputo (ABC) sense in the form of a non-singular kernel. The model is solved by using numerical techniques. It is seen that the myeloid cell population significantly affects the stem cell population.

KW - Cell production system

KW - Non-singular kernel

KW - Stability analysis

KW - Stem cell

UR - https://www.scopus.com/pages/publications/85122409405

U2 - 10.3934/math.2022289

DO - 10.3934/math.2022289

M3 - Article

AN - SCOPUS:85122409405

SN - 2473-6988

VL - 7

SP - 5175

EP - 5198

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 4

ER -

Fractional order modeling and analysis of dynamics of stem cell differentiation in complex network

Abstract

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Keywords

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