HEMATOPOIETIC MODEL WITH MOVING BOUNDARY-CONDITION AND STATE-DEPENDENT DELAY - APPLICATIONS IN ERYTHROPOIESIS

An age-structured model for erythropoiesis is extended to include the active destruction of the oldest mature cells and possible control by apoptosis. The former condition, which is applicable to other populati on models where the predator satiates, becomes a constant flux boundar y condition and results in a moving boundary condition. The method of characteristics reduces the age-structured model to a system of thresh old type differential delay equations. Under certain assumptions, this model can be reduced to a system of delay differential equations with a state dependent delay in an uncoupled differential equation for the moving boundary condition. Analysis of the characteristic equation fo r the linearized model demonstrates the existence of a Hopf bifurcatio n when the destruction rate of erythrocytes is modified. The parameter s in the system are estimated from experimental data, and the model is simulated for a normal human subject following a loss of blood typica l of a blood donation. Numerical studies for a rabbit with an induced auto-immune hemolytic anemia are performed and compared with experimen tal data. (C) 1998 Academic Press Limited.