Mathematical model for the growth of a tumour taking into account an immune response of the organism

The paper describes a predictive mathematical model capable of taking into account the complex multicomponent process of interaction of the immune system elements in the event of the appearance of abnormal cells caused by a violation of its synthetic function. The importance of the mathematical simulation application is conditioned by the fact that existing statistical methods do not allow one to fully estimate the effects caused by the functional disorders’ accumulation process in the body systems due to the limitations on the development and experimentations. 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. Modelling takes into account the functional state of the studied organs. 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. To solve the obtained Cauchy Problem, the implicit numerical 3rd order Runge-Kutta Method is used. A number of computational experiments on tumor growth have been performed. The constructed model makes it possible to show the mechanics of the multicomponent interaction of the immune system during the emergence and growth of malignant tumors under the influence of the environment.