TY - JOUR
T1 - On the global dynamics of one cancer tumour growth model
AU - Starkov, Konstantin E.
AU - Krishchenko, Alexander P.
N1 - Funding Information:
The work of the second author was supported by the Russian Foundation for Basic Research (project N. 13-07-00720 and N. 11-01-00733).
PY - 2014/5
Y1 - 2014/5
N2 - 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.
AB - 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.
KW - Cancer tumour model
KW - Positively invariant domain
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84887828220&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2013.09.023
DO - 10.1016/j.cnsns.2013.09.023
M3 - Artículo
SN - 1007-5704
VL - 19
SP - 1486
EP - 1495
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
IS - 5
ER -