  We present a phase-space analysis of a mathematical model of tumor growth
with an immune responses. We consider mathematical analysis of the model
equations with multipoint initial condition regarding to dissipativity,
boundedness of solutions, invariance of non-negativity, local and global
stability and the basins of attractions. We derive some features of behavior of
one of three-dimensional tumor growth models with dynamics described in terms
of densities of three cells populations: tumor cells, healthy host cells and
effector immune cells. We found 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
points-the healthy equilibrium point, the "death" equilibrium point have been
examined. Biological implications of our results are discussed.
