ON A NONLINEAR SYSTEM MODELING DARWINIAN DYNAMICS AND THE IMMUNE RESPONSE TO CANCER EVOLUTION

摘要

In this paper a mathematical model, at the cellular level, related to the onset and evolution of cancer cells contrasted by the immune system, is derived by tools of kinetic theory of active particles, for short KTAP's approach. The dynamics refers to an early stage of the competition, where cancer is viewed as sequence of phenotype mutations, which generate cells with the ability of suppressing the innate programmed death ability-apopthosis- on one side and on the other with the ability to escape recognition by immune cells. The subsequent dynamics of selection and competition for survivance determines the growth or depletion of tumor cells. The originated model introduced in Ref. 13,which has been further developed in Ref. 20 to include interactions with the outer environment, which can also be subject to mutation and selection1~(16,24). More specifically, we develop an analytic study of the well-posdenes of the initial value problem, and we will investigate numerically how our model depict some interesting behaviors of the immune response, where some biological interpretations are discussed.