Bioautomation (Dec 2008)
Reduction of Dimensionality of a Dynamical Model of Aggressive Tumor Treated by Chemotherapy, Immunotherapy and siRNA Infusion. Part І. Establishment of Time Hierarchy in the Model Dynamics
Abstract
The Tichonov's theorem for quasi-stationary approximation is considered as a basic approach for reduction of dynamical systems with time hierarchy. On the basis of previously determined parameters, seven ordinary differential equations of the dynamical model of tumor treated by chemotherapy, immunotherapy and siRNA infusion are written in a form appropriate to evaluate their terms for model reduction. In accordance with the terminology of the Tichonov's theorem, it is established that three of the system components are fast varying such that the corresponding kinetic equations form an attached system. The other four variables are slow varying and their kinetic equations form a degenerate system
