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.