A Novel Nonlinear Dynamic Model Describing the Spread of Virus

Veli B. Shakhmurov; Muhammet Kurulay; Aida Sahmurova; Mustafa Can Gursesli; Antonio Lanata

doi:10.3390/math11204226

A Novel Nonlinear Dynamic Model Describing the Spread of Virus

Veli B. Shakhmurov
, Muhammet Kurulay
, Aida Sahmurova
, Mustafa Can Gursesli
, Antonio Lanata^*

^*Corresponding author for this work

Antalya Bilim University
Azerbaijan State University of Economics
Yildiz Technical University
University of Florence

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

2 Citations (Scopus)

Abstract

This study proposes a nonlinear mathematical model of virus transmission. The interaction between viruses and immune cells is investigated using phase-space analysis. Specifically, the work focuses on the dynamics and stability behavior of the mathematical model of a virus spread in a population and its interaction with human immune system cells. The endemic equilibrium points are found, and local stability analysis of all equilibria points of the related model is obtained. Further, the global stability analysis, either at disease-free equilibria or in endemic equilibria, is discussed by constructing the Lyapunov function, which shows the validity of the concern model. Finally, a simulated solution is achieved, and the relationship between viruses and immune cells is highlighted.

Original language	English
Article number	4226
Journal	Mathematics
Volume	11
Issue number	20
DOIs	https://doi.org/10.3390/math11204226
Publication status	Published - Oct 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023 by the authors.

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

immune system
mathematical modeling
stability of dynamical systems
virus

Access to Document

10.3390/math11204226

Cite this

@article{ce10dbab34f74a00b68cd5753fea26ce,

title = "A Novel Nonlinear Dynamic Model Describing the Spread of Virus",

abstract = "This study proposes a nonlinear mathematical model of virus transmission. The interaction between viruses and immune cells is investigated using phase-space analysis. Specifically, the work focuses on the dynamics and stability behavior of the mathematical model of a virus spread in a population and its interaction with human immune system cells. The endemic equilibrium points are found, and local stability analysis of all equilibria points of the related model is obtained. Further, the global stability analysis, either at disease-free equilibria or in endemic equilibria, is discussed by constructing the Lyapunov function, which shows the validity of the concern model. Finally, a simulated solution is achieved, and the relationship between viruses and immune cells is highlighted.",

keywords = "immune system, mathematical modeling, stability of dynamical systems, virus",

author = "Shakhmurov, \{Veli B.\} and Muhammet Kurulay and Aida Sahmurova and Gursesli, \{Mustafa Can\} and Antonio Lanata",

note = "Publisher Copyright: {\textcopyright} 2023 by the authors.",

year = "2023",

month = oct,

doi = "10.3390/math11204226",

language = "English",

volume = "11",

journal = "Mathematics",

issn = "2227-7390",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "20",

}

TY - JOUR

T1 - A Novel Nonlinear Dynamic Model Describing the Spread of Virus

AU - Shakhmurov, Veli B.

AU - Kurulay, Muhammet

AU - Sahmurova, Aida

AU - Gursesli, Mustafa Can

AU - Lanata, Antonio

PY - 2023/10

Y1 - 2023/10

N2 - This study proposes a nonlinear mathematical model of virus transmission. The interaction between viruses and immune cells is investigated using phase-space analysis. Specifically, the work focuses on the dynamics and stability behavior of the mathematical model of a virus spread in a population and its interaction with human immune system cells. The endemic equilibrium points are found, and local stability analysis of all equilibria points of the related model is obtained. Further, the global stability analysis, either at disease-free equilibria or in endemic equilibria, is discussed by constructing the Lyapunov function, which shows the validity of the concern model. Finally, a simulated solution is achieved, and the relationship between viruses and immune cells is highlighted.

AB - This study proposes a nonlinear mathematical model of virus transmission. The interaction between viruses and immune cells is investigated using phase-space analysis. Specifically, the work focuses on the dynamics and stability behavior of the mathematical model of a virus spread in a population and its interaction with human immune system cells. The endemic equilibrium points are found, and local stability analysis of all equilibria points of the related model is obtained. Further, the global stability analysis, either at disease-free equilibria or in endemic equilibria, is discussed by constructing the Lyapunov function, which shows the validity of the concern model. Finally, a simulated solution is achieved, and the relationship between viruses and immune cells is highlighted.

KW - immune system

KW - mathematical modeling

KW - stability of dynamical systems

KW - virus

UR - https://www.scopus.com/pages/publications/85175581937

U2 - 10.3390/math11204226

DO - 10.3390/math11204226

M3 - Article

AN - SCOPUS:85175581937

SN - 2227-7390

VL - 11

JO - Mathematics

JF - Mathematics

IS - 20

M1 - 4226

ER -

A Novel Nonlinear Dynamic Model Describing the Spread of Virus

Abstract

Bibliographical note

UN SDGs

Keywords

Access to Document

Other files and links

Fingerprint

Cite this