Gvozdetska I. Mathematical models of tumor growth based on the Gompertz dynamics.

The thesis is devoted to the mathematical modeling of the processes of tumor growth based on the Gompertz dynamics. The existence of positive and stability of solutions for a generalized model based on Gompertz dynamics are investigated. A model of antitumor immunity with impulsive perturbations with respect to the population of proliferating cells is proposed. The asymptotic estimates of are obtained for solutions of the equations. The estimates are based on impulsive differential inequalities for Lyapunov-type functions. The existence of the periodic solution of a system with the absence of immunity is proved in the thesis. The conditions for its global asymptotic stability are obtained. The model of immunotherapy is proposed. The control of the process of tumor growth in a class of differential equations of Gompertz dynamics are improved. The problem of optimal control in the model chemoradiation and immunotherapy is considered. On the basis of principles and approaches to computer simulation and based on existing software that is used in biomedical research suggested Web-integrated software environment that implements the basic mathematical model of tumor growth based on Gompertz dynamics.