Analysis of One Model of the Immune System - Kavaliauskas, A. (Nonlinear Analysis: Modelling and Control, 2003)
The article deals with development of a tumor in the cylindrical space. A model with two parameters – lymphocytes and tumor cells – described in [1] is taken as a base of the research. Some generalization of the model is done. The research, results of which are described in [2, 3], was continued. The relationship between the surface and volumetric tumor cells of classical forms is obtained. It turns out, that even in general case the trivial stationary point is of a saddle type.The article particularly deals with the development of a cylindrical tumor. It is considered, that lymphocytes and the medical intervention (chemotherapy or irradiation) keeps down the cell fission of the tumor. Some special parameter is introduced to indicate the influence of the medical cure. In respect of that parameter the bifurcation values of the system are surveyed using the theory of [1, 4]. Some results of the survey are tested with the help of the software package MAPLE.
Keywords: immune system; tumor cells; cylindrical surrounding; Hopf bifurcation