The local and global dynamics of a cancer tumor growth and chemotherapy treatment model (1803.05330v1)

Abstract: 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.