On the global dynamics of one cancer tumour growth model

• Global dynamics of de Pillis–Radunskaya tumour growth model is examined.
• Upper and lower bounds for the effector immune cells population is got.
• Conditions for which all trajectories tend to one of equilibrium points are given.
• Here various cases of biologically feasible equilibrium points are studied.

In this paper we study some features of global behavior of one three-dimensional tumour growth model obtained by de Pillis and Radunskaya in 2003, with dynamics described in terms of densities of three cells populations: tumour cells, healthy host cells and effector immune cells. We find the upper and lower bounds for the effector immune cells population, with t→∞t→∞. Further, we derive sufficient conditions under which trajectories from the positive domain of feasible initial conditions tend to one of equilibrium points. Here cases of the small tumour mass equilibrium point; the healthy equilibrium point; the “death” equilibrium point are examined. Biological implications of our results are considered.