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 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.

Automated summary

This study utilized phase-space analysis to investigate the interaction between virus and immune response in a mathematical model of tumor growth. A dynamic model was used to mathematically determine the relationship between uninfected cells, infected cells, effector immune cells, and free viruses. Stability analysis of the system and the Lyapunov stability of the equilibrium points were revealed, and all endemic equilibrium point models were derived. The stability behavior and range of attraction sets of the nonlinear systems in our model were investigated. Furthermore, a global stability analysis was proven for both disease-free equilibria and endemic equilibria.