A Novel Nonlinear Dynamic Model Describing the Spread of Virus

Veli B. Shakhmurov, Muhammet Kurulay, Aida Sahmurova, Mustafa Can Gursesli and Antonio Lanata ()
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Veli B. Shakhmurov: Department of Industrial Engineering, Antalya Bilim University, Ciplakli Mahallesi Farabi Caddesi 23 Dosemealti, 07190 Antalya, Turkey
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
Antonio Lanata: Department of Information Engineering, University of Florence, Via Santa Marta 3, 50139 Florence, Italy

Mathematics, 2023, vol. 11, issue 20, 1-15

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: mathematical modeling; virus; immune system; stability of dynamical systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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