Dinâmica não linear em modelos de tratamento de leucemia

Abstract

In this work, we performed a qualitative study of a model consisting of three ordinary differential equations that describe the interaction between leukemic stem cells and immune cells, where the immune functional response against leukemia exhibits an optimal activation window. We investigated the stability of the equilibrium points with respect to the system parameters and the existence of bifurcations. We rigorously demonstrate that the model exhibits at least two types of bifurcations. The first is the transcritical bifurcation around the tumor-free equilibrium point. The second is the Hopf bifurcation around a biologically plausible equilibrium point. We focused our attention on the latter, examining the emergence of limit cycles and analyzing their stability through the sign of the Lyapunov coefficient. We verified the theoretical results through numerical simulations using the Mathematica software.