Interaction of Virus in Cancer Patients: A Theoretical Dynamic Model

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...

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Bibliographic Details
Published in:Bioengineering (Basel) 2023-02, Vol.10 (2), p.224
Main Authors: Shakhmurov, Veli B, Kurulay, Muhammet, Sahmurova, Aida, Gursesli, Mustafa Can, Lanata, Antonio
Format: Article
Language:English
Subjects:
Bioengineering
Cancer
Cancer patients
Cancer therapies
Chemotherapy
COVID-19 vaccines
Disease prevention
Dynamic models
Dynamic stability
Effector cells
Epidemics
Epidemiology
Host-virus relationships
Immune response
Immune system
immune system cells
Infections
Liapunov functions
Mathematical analysis
mathematical modeling
Mathematical models
Nonlinear systems
Observations
Partial differential equations
Physiological aspects
Quarantine
Stability analysis
stability of dynamical systems
Systems stability
tumor growth
Viral infections
virus
Viruses
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Summary: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.
ISSN:2306-5354
2306-5354
DOI:10.3390/bioengineering10020224