Oncogenesis mathematical model in the concept of cancer stem cells

Oncological diseases are widespread at present time. Mathematical modeling for these diseases provides an answer to the question of a person's expectancy of life depending on a certain therapy. The paper provides a brief analysis of the functional load of cancer stem cells in the general system of the cancer cell population. This analysis includes consideration under conditions of an immune response and external influence (chemotherapy). The neoplasm growth modeling and the immune response to the disease, a model of the growth of a neoplasm during immune response and chemotherapy are proposed taking into account the approaches outlined in the literature. Mathematical models of neoplasms based on the positions of the clonal concept (Burnet's theory), which take into account the growth of cancer (dividing) cells, the response of the immune system, and drug therapy, these models are described by the Cauchy problem for a system of ordinary differential equations. The dynamics of tumor growth are determined based on the model. The model of disease stages is based on the distribution of the main parameters that determine the kinetics growth of the dividing cells population. An estimate is given of the average time to reach four stages of the disease and the duration of remission after the end of treatment using a statistical approach. The obtained theoretical results are compared with the data of the Russian Population Cancer Registry.

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