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 journalArticlepeer-review


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 languageEnglish
Article number4226
Issue number20
Publication statusPublished - Oct 2023
Externally publishedYes

Bibliographical note

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© 2023 by the authors.


  • immune system
  • mathematical modeling
  • stability of dynamical systems
  • virus


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