Effects of Immune Response and Time Delays in Models of Acute Myeloid Leukaemia

Abstract

In this paper, we propose a general acute myeloid leukaemia (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 bi-stability of the steady states, and a stronger response wipes out all the leukaemia cells. In addition, we further reveal that the time delays existing in the feedback regulation and immune response process induce a series of oscillations around the steady state, which shows that the leukaemia cells can hardly be 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.