Modelling and Stability Analysis of (TIV) System Using Lyapunov Function

Abstract

Tumour Immune Virus (TIV) model is theoretically analysed based on a system of five nonlinear ordinary differential equations (NODEs). The model is divided into five compartmental classes: uninfected cancer cells , virus-infected cancer cells  immune effector cells  dead cells  and free virus particles . The aim is to investigate the stability of the deterministic TIV model both analytically and numerically, utilising the Lyapunov function and the Runge-Kutta-Fehlberg (RKF) method. For the deterministic model, five steady points are derived, and their local and global stability are investigated for the coexistence steady point; however, specific criteria were employed to confirm the existence and stability of these steady states. Also, numerical simulations were conducted to study the dynamic behaviour of the TIV system, whose findings offer more insights into the impact of oncolytic treatment on the immune response and contribute to the development of more effective strategies.