Homeostatic control for regulation of neutrophil production

In the above equations, soi wo, and eo denote history and initial conditions corresponding to the undisturbed state of the process at equilibrium. 

we propose to study a model with delayed feedback, as done by several investigators [47,48,485-487,495-499]. 

Normally, the equilibrium behavior of the process requires that the production rate equal the disappearance rate. These conditions and the introduction of the variable transformation g (t) = as (t) allows us to determine the input rates Rs and Re  

Current analytic and numerical work determine the time-dependent changes in blood cell number as certain quantities, referred to as control parameters, are varied. Examples of control parameters in the regulation of hemopoiesis are the dimensionless maturation time r° and the peripheral destruction rates 7 and A. 

It is well established that under appropriate circumstances, delayed negative feedback mechanisms can produce oscillations. To illustrate this point we continue with the stability analysis. 

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Figure 11.5 Homeostatic control for regulation of neutrophil production. Parameters are wq = 4 and eo = 1 cellsxlO6 ml-1, = 2 and 6=1, and kw = 0.7 d-1. o indicates the position of the equilibrium point.

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