The evolution of a michaelis-menten type dynamics of tum
Özet
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, ..., tm and correlated.
Mathematical analysis of the Michaelis-Menten 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 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.