Numerical modelling of the reaction of the immune system to the tumor based on the revised model of Resigno and de Lisi

The article is devoted to the modelling of the immune response for the presence of cancer at initial stage. At this stage the key role in the development of disease is given to the immune system. It is the immunological insufficiency that is a major cause of high incidence of malignant neoplasms. The article describes the mathematical model of the immune response to the tumor. The presented model is based on the mathematical model of Resigno and De Lisi. In the created model, unlike the classical one, we take into account the fact that the presence of cancer overwhelmingly affects the immune system, and assumes the possibility of introducing of outside lymphocytes for immune response stimulation. This article provides an example of numerical prediction of tumor development, based on the constructed model. In addition the paper describes an algorithm for determining of the optimal level of input lymphocytes. The algorithm is based on the analysis of singular points of the system and numerical simulation.