Dynamics of a Mathematical Model of Cancer and Immunoediting Scenarios Under the Variation of the Immune Cell Activation Rate

Abstract

This article investigates the dynamics of cancer through a coupled system of three nonlinear ordinary differential equations. The evolution of the cancer tumour is examined under the variation of the immune cell activation parameter, and the study determines the values of this parameter that cause changes in the dynamics of this evolution; these changes are a consequence of two transcritical bifurcations and a supercritical Hopf bifurcation that exist in the system. These results reveal the range of immune cell activation for which tumour escape or tumour latency, or oscillatory behavior due to the appearance of limit cycles, is achieved. In addition, an optimal value is distinguished for which a minimum number of active immune response cells is sufficient to bring the tumour to a latent state.