A dynamical model of the immune system interaction in a melanoma

Abstract

Melanoma is a concerning variety of skin cancer which prevalence arises in our society. Its lethality relies on its ability to migrate and metastasize. In this paper, we use a mathematical model of tumor growth and lysis, and we adjust it to model melanoma growth. Tumor growth is modeled through the action of a cellular automaton and two reaction–diffusion equations for nutrients distribution. In order to represent the melanoma, we have induced mutations in random cells, specifically in their reproductive capacity, so that tumor growth appears less structured and consistent. A coherent mathematical model for the decay of the melanoma has been created by means of an exponential function. The results show that the inner morphology plays an important role in cancer lysis: as the complexity increases, so does lysis time. We have also compared simulations to real melanomas with the aim of acknowledging the robustness of the melanoma modeling.