On the global dynamics of one cancer tumour growth model

Konstantin E. Starkov, Alexander P. Krishchenko

Research output: Contribution to journalArticle

26 Scopus citations


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 languageAmerican English
Pages (from-to)1486-1495
Number of pages1336
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - 1 May 2014
Externally publishedYes


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