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The article is devoted to the study of the regulatory mechanisms dynamics of skin carcinoma on the basis of the firmly established facts and theoretical positions in the field of biology, biophysics and regulation. The developed equations for the regulatory mechanisms of skin cells transformation into abnormal cancer cells have a functional-differential type. Implementation of the developed equations for the epidermis cellular communities number regulation in squamous cell carcinoma on a computer and a series of computational experiments have shown that these equations have stable stationary, self-oscillating solutions typical for the normal functioning of the skin; have chaotic solutions and the “black hole” effect, which makes it possible to diagnose the onset of the phase of unpredictable changes in the skin epidermis regulation and the beginning of the transition into tumor cells. Mathematical and computer models of the skin epidermis regulation at the norm and at the tumor process can be used to improve the methods of early diagnosis, prevention of skin diseases, as well as to choose treatment tactics.

The article considers mathematical modeling of regulatory mechanisms of the cardiovascular system, based on the method of functional differential equations of cardiac regulation and equations for the quantitative description of blood movement in vessels and tissues using the reduced Navier-Stokes equations and the equations of active and passive transfers in normal and in case of tumor processes in human organs. The results of computational experiments showed the presence of five areas of functioning: a trivial attractor, stationary mode, stable oscillations with a constant period, irregular oscillations (a risk zone for life-threatening arrhythmias during chemical and radiation therapy) and a “black hole” (sudden cardiac death during antitumor treatment).

New methods for analyzing clinical data for oncological patients are developed. These data are considered as observed variables of the mathematical tumor model. The connection between a mortality index and individual dynamics of the observed data is discussed. This approach allows the clinically unexpressed part of the tumor process to be observed, and it also allows the process to be examined during treatment. >