A dynamic model of interactions between tumor growth and the immune response

Abstract

This work presents a simple mathematical model of the interaction of a tumor cell population with the $T$-lymphocyte immune response in the perspective of an immunotherapy by immune checkpoint inhibitors. We first characterize the existence of the steady states. We then decompose parameter space into distinct regions according to the linear stability of the coexistence steady state, as well as identify regions of parameter space in which a Hopf bifurcation exists. Finally, we present numerical results which confirm the predicted stability of the steady state solutions.