Mathematical model of antitumor immune response of organism regulation

A predictive mathematical model capable to describe a complex multicomponent process of interaction of the immune system elements under occurring of the abnormal tissue cells that is reasoned by its synthetic function violation is demonstrated by this work. The model has been developed within the concept of the multi-level model of the human organism and is targeted to describe the different-scale processes occurring during the development of cancer. The structural chart of the model includes the following elements: tissue cells, characterized by a set of parameters, and a set of interrelated components of the immune system, which are the most important components in the body's response to the formation of cancer cells. Modelling takes into account the functional state of the studied organs. As the factors, having impact on the state changes, natural aging and the negative effects of diverse chemicals entering from the environment can be distinguished. Building on the created interaction scheme, the ordinary differential equations are written, which are described by the First Order ODE’s with lags of the argument. A number of computational experiments on tumor growth have been performed. The obtained calculated data on the dynamics of changes in the characteristics of the cell populations of the tissue under consideration in individual points and in the entire volume as a whole have been analyzed.