Effects of immune response and time delays in models of acute myeloid leukemia

In this paper, we propose a general acute myeloid leukemia (AML) model and introduce an immune response and time delays into this model to investigate their effects on the dynamics. Based on the existence, stability and local bifurcation of three types of equilibria, we show that the immune response is a best strategy for the control of the AML on the condition that the rates of proliferation and differentiation of the hematopoietic lineage exceed a threshold. In particular, a powerful immune response leads to a bistability feature meaning there exist the leukemia cells and healthy cells in the bone marrow or only the healthy cells. In addition, we further reveal that the time delays in the feedback regulation and immune response process induce a series of oscillations around the steady state, which shows that the leukemia cells are hardly eliminated. Our work in this paper aims to investigate the complex dynamics of this AML model with the immune response and time delays on the basis of mathematical models and numerical simulations, which may provide a theoretical guidance for the treatments of the AML.