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→ ∞. 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. © 2013 Elsevier B.V.
|Original language||American English|
|Number of pages||1336|
|Journal||Communications in Nonlinear Science and Numerical Simulation|
|State||Published - 1 May 2014|
Starkov, K. E., & Krishchenko, A. P. (2014). On the global dynamics of one cancer tumour growth model. Communications in Nonlinear Science and Numerical Simulation, 1486-1495. https://doi.org/10.1016/j.cnsns.2013.09.023