Shakhmurov VB, Kurulay M, Sahmurova A, Gursesli MC, Lanata A. Interaction of Virus in Cancer Patients: A Theoretical Dynamic Model.
Bioengineering (Basel) 2023;
10:bioengineering10020224. [PMID:
36829718 PMCID:
PMC9952378 DOI:
10.3390/bioengineering10020224]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2023] [Revised: 01/30/2023] [Accepted: 02/01/2023] [Indexed: 02/11/2023] Open
Abstract
This study reports on a phase-space analysis of a mathematical model of tumor growth with the interaction between virus and immune response. In this study, a mathematical determination was attempted to demonstrate the relationship between uninfected cells, infected cells, effector immune cells, and free viruses using a dynamic model. We revealed the stability analysis of the system and the Lyapunov stability of the equilibrium points. Moreover, all endemic equilibrium point models are derived. We investigated the stability behavior and the range of attraction sets of the nonlinear systems concerning our model. Furthermore, a global stability analysis is proved either in the construction of a Lyapunov function showing the validity of the concerned disease-free equilibria or in endemic equilibria discussed by the model. Finally, a simulated solution is achieved and the relationship between cancer cells and other cells is drawn.
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