SDC-method in Problem's Develop of Strategy of Cancer Therapy

This work includes the description of a method of "extendend linearization" and one of ways of finding of optimum control for nonlinear system on the example of a problem of introduction of preparations at a cancer therapy. As this problem is actual in the world and causes huge interest from outside not only physicians, but also mathematicians, physicists and other scientists at the moment there is the whole massif of mathematical models of development of cancer and its treatment, each of which includes interaction of cancer and immune cells, cancer and healthy cells, cancer cells and therapy. In work the model stated in the article of L. G. dePillis, A. E. Radunskaya "Mathematical Models of Tumor-Immune System Dynamics", Springer Proceedings in Mathematics & Statistics, 107, 59-109, 2014 which describes dynamics of process of growth of cancer fabric and its interaction both with normal, and with immune cages is used. The main complexity is represented by the fact that the model contains the nonlinear differential equations, and her linearization can lead to negative consequences which physical sense consists in increase in toxicity of treatment, emergence of threat for life of the patient or rendering harm to healthy bodies is a consequence of what. For check of efficiency all received the decision mathematical modeling which results are also given in this work has been carried out.