STABILITY FEATURES OF THE DYNAMICAL SYSTEM EMERGING IN THE MODEL OF THE CANCER GROWTHV. SHAKHMUROV, A. MAHARRAMOV, A. SAHMUROVA (pp. 23-40)
Abstract.In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth kinetics in the impedimental conditions created by related immune responses and chemotherapy agents. Mathematical modeling of such a complicated processes appeared potentially very powerful tool for the development of some of the improved treatment regimens. Mathematical analysis of the model equations, encapsulating multipoint initial conditions with regard to such a problems as dissipativity, boundedness of solution, invariance of non-negativity, nature of equilibria, local and global stability have been investigated. We studied some of the features of behavior of a three dimensional tumor growth model in dynamics - kinetics of changes - depended on cell population densities of tumor cells, healthy host cells, effector immune cells and chemical agents.
Keywords:mathematical modeling, tumor dynamics, immune system, stability, dynamical systems, drug treatment.