Stability of a model of human granulopoiesis using continuous maturation

A class of mathematical models involving a convection-reaction partial differential equation (PDE) is introduced with reference to recovering human granulopoiesis after high dose chemotherapy with stem cell support. The stability properties of the model are addressed by means of numerical investigations and analysis. A simplified model with proliferation rate and mobilization rate independent of maturity shows that the model is stable as the maturation rate grows without bounds, but may go through stable and non-stable regimens as the maturation rate varies. It is also shown that the system is stable when parameters are chosen to approximate a real physiological situation. System characteristics do not change profoundly by introduction of a maturity-dependent proliferation and mobilization rate, as is necessary to make the model operate more in accordance with hematological observations. However, by changing the system mitotic responsiveness with respect to changes in cytokine level, the system is still stable but may show persistent oscillations much resembling clinical observations of cyclic neutropenia. Furthermore, in these cases, changes in the model feedback signal caused by, for instance, an impaired effective cytokine elimination by cell receptors may enforce these oscillations markedly.