  In this paper, we studied phase-space analysis of a certain mathematical
model of tumor growth with an immune responses and chemotherapy therapy.
Mathematical modelling of this process is viewed as a potentially powerful tool
in the development of improved treatment regimens. Mathematical analysis of the
model equations with multipoint initial condition, regarding nature of
equilibria, local and global stability have been investigated. We studied 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. The addition
of a drug term to the system can move the solution trajectory into a desirable
basin of attraction. We show that the solutions of the model with a
time-varying drug term approach can be evaluated more fruitful way and down to
earth style from the point of practical importance than the solutions of the
system without drug treatment, in the condition of stimulated immune processes,
only.
