Stability Analysis Tumour Growth Model with Interphase Delay: A Computational Study

Purpose: In this manuscript, we study a mathematical model of the tumor cell cycle with delay to understand and improve patient quality of life, and design better treatment strategies.Design/Methodology: This study investigates the system of differential equations to the represent the cell cycle progression in tumour growth model with interphase delay. This analysis seeks to determine the competition model of immune system react cell cycle progression of a specific drug of cycle phase. This theoretical analysis utilized to find impact of immune response, and the effects of specific drugs in cycle-phase and bifurcation analysis in biological process.Findings: We demonstrate the influence of delay and the stability of the tumor growth with delay differential equation model. The tumor population is stable within 20 days without delay. But in the presence of delay, the tumor growth is stable around 120 days. Increased interphase duration enhanced the rate of cell death in mitosis, and potential drug resistance. Without drug and immune cells, tumor growth is unstable and reaching 10 × 106 cells around 160 days in interphase.Originality/values: This study presents a novel investigation into the stability of delay differential equations for tumor population. We explore new territory in tumor growth model with interphase delay by considering cell cycle that have not been thoroughly examined in prior studies despite their obvious relevance.