A mathematical model, coupling the dynamics of short-term stem-like cells and mature
leukocytes in leukemia with that of the immune system, is investigated. The model is
described by a system of seven delay differential equations with seven delays. Three
equilibrium points E0, E1,
E2 are highlighted. The stability and the existence of the
Hopf bifurcation for the equilibrium points are investigated. In the analysis of the
model, the rate of asymmetric division and the rate of symmetric division are very
important.