The evolution of a michaelis-menten type dynamics of tumor growth model

Abstract

Here, we investigate Michaelis-Menten type dynamics of phase-space analysis to a mathematical model of tumor growth with an immune responses. We then explore the effects of adaptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The addition of a drug term to the system can move the solution trajectory into a desirable basin of attraction. One of main aims is derivation of sufficient conditions under which the possible biologically feasible dynamics is local and globally stable, and a converges to one of equilibrium points. Since these equilibrium points have a biological sense, we notice that understanding limit properties of dynamics of cells populations based on solving problem nonlinear dynamical system may be of an essential interest for the prediction of health conditions of a patient without a treatment, when the data (e.g. the status of blood cells shown above) that determines the condition of the patient are compared at various times t₀,t₁,...,t_{m} and correlated. Mathematical analysis of the MichaelisMenten type equations, regarding to dissipativity, boundedness of solutions, nature of equilibria, local and global stability have been investigated. We studied some features of behavior of one of threedimensional tumor growth models with dynamics described in terms of densities of three cells populations: tumor cells, healthy host cells and effector immune cells.