Tumour-Immune Interaction Model with Cell Cycle Effects Including G0 Phase

Abstract

Tumour cells behave differently than normal cells in the body. They grow and divide in an uncontrolled manner (actively proliferating) and fail to respond to signal. However, there are cells that become inactive and reside in quiescent phase (G0). These cells are known as quiescence cells that are less sensitive to drug treatments (radiotherapy and chemotherapy) than actively proliferation cells. This paper proposes a new mathematical model that describes the interaction of tumour growth and immune response by considering tumour population that is divided into three different phases namely interphase, mitosis and G0. The model consists of a system of delay differential equations where the delay, represents the time for tumour cell to reside interphase before entering mitosis phase. Stability analysis of the equilibrium points of the system was performed to determine the dynamics behaviour of system. Result showed that the tumour population depends on number of tumour cells that enter active (interphase and mitosis) and G0phases. This study is important for treatment planning since tumour cell can resist treatment when they refuge in a quiescent state.