Modeling cancer evolution: Evolutionary escape under immune system control

It can be expected that adequate immune response should be able to annihilate cancer at a very early stage of its appearance. However, in some cases cancer is able to persist avoiding immune response. One can conject that cancer is able to avoid immune response control due to a succession of mutations leading to the development of immune-resistant cells. In order to illustrate this possibility, in this paper we present a 2n-dimensional mathematical model that describes interaction of n subtypes of tumor cells with corresponding genotype-specific immune response. The model postulates that there is a probability for tumor cells of each of n subtype to produce offsprings of other types. Each of the subtypes activates the genotype-specific immune response with a possibility of suppressing cancer cells of other genotypes (the cross-immunity). Numerical simulations show that if cancer cells are able to mutate comparatively fast and if immune response is not strong enough, then, despite immune system pressure, cancer is able to persist.