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

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

1 Citation (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.

Keywords

immune system
mathematical modeling
stability of dynamical systems
virus

UN SDGs

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

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10.3390/math11204226

Cite this

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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.",

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

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volume = "11",

journal = "Mathematics",

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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

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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

Keywords

UN SDGs

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