Resumo:
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.
