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This paper deals with the modeling of the immune response to the evolution of the progression of endothelial cells which have lost the differentiation and start their evolution towards metastatic states. The modeling is developed in the framework of the so-called kinetic cellular theory. The model is critically analyzed on the basis of analytic solutions, asymptotic behaviors and numerical simulations that illustrate the scenarios predicted by the model. Finally, possible developments and generalizations that could describe other known phenomena are pointed out. [ABSTRACT FROM AUTHOR]

Marchuk's model of a general immune reaction is presented in the paper. The results of investigation of the model are summarized. The qualitative behaviour of solutions to the model and its simplification is described. Many illustrations of recovery process, oscillations or lethal outcomes of a disease are shown. The model with time-dependent immune reactivity is also considered. Periodic dynamics caused by different reasons are compared. In the last section adaptation of the model to tumour-immune interactions is proposed. The role of interleukins in immune processes is taken into account to adapt Marchuk's model to tumour growth dynamics. Possible immunotherapy is also considered in the proposed model. Some preliminary analysis of the model is presented. [ABSTRACT FROM AUTHOR]