On the dynamics of a cancer tumor growth model with multiphase structure

In this paper, we study a phase-space analysis of a mathematical model of tumor growth with an immune response. Mathematical analysis of the model equations with multipoint initial condition, regarding to dissipativity, boundedness of solutions, invariance of non-negativity, nature of equilibria, local and global stability will be investigated. We study some features of behavior of one three-dimensional tumor growth model with dynamics described in terms of densities of three cells populations: tumor 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 multipoint initial conditions tend to one of equilibrium points. Here cases of the small tumor mass equilibrium point; the healthy equilibrium point; the “death” equilibrium point are examined. Biological implications of our results are considered.