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A Novel Nonlinear Dynamic Model Describing the Spread of Virus

Author

Listed:
  • Veli B. Shakhmurov

    (Department of Industrial Engineering, Antalya Bilim University, Ciplakli Mahallesi Farabi Caddesi 23 Dosemealti, 07190 Antalya, Turkey
    Center of Analytical-Information Resource, Azerbaijan State Economic University, 194 M. Mukhtarov, AZ1001 Baku, Azerbaijan)

  • Muhammet Kurulay

    (Department of Mathematics Engineering, Yildiz Technical University, 34225 Istanbul, Turkey)

  • Aida Sahmurova

    (Department of Nursing, Antalya Bilim University, Ciplakli Mahallesi Farabi Caddesi 23 Dosemealti, 07190 Antalya, Turkey)

  • Mustafa Can Gursesli

    (Department of Information Engineering, University of Florence, Via Santa Marta 3, 50139 Florence, Italy
    Department of Education, Literatures, Intercultural Studies, Languages and Psychology, University of Florence, 50135 Florence, Italy)

  • Antonio Lanata

    (Department of Information Engineering, University of Florence, Via Santa Marta 3, 50139 Florence, Italy)

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.

Suggested Citation

  • Veli B. Shakhmurov & Muhammet Kurulay & Aida Sahmurova & Mustafa Can Gursesli & Antonio Lanata, 2023. "A Novel Nonlinear Dynamic Model Describing the Spread of Virus," Mathematics, MDPI, vol. 11(20), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4226-:d:1256563
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    References listed on IDEAS

    as
    1. C. P. Farrington & N. J. Andrews & A. D. Beale & M. A. Catchpole, 1996. "A Statistical Algorithm for the Early Detection of Outbreaks of Infectious Disease," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 159(3), pages 547-563, May.
    2. Bekiros, Stelios & Kouloumpou, Dimitra, 2020. "SBDiEM: A new mathematical model of infectious disease dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
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