Now we suppose that the production of red blood cells is controlled by N, and that once a cohort of cells is formed in the bone marrow, they will emerge into the bloodstream as mature cells some fixed time d later, about 5 days. Here we are ignoring the fact that at high levels of erythropoietin (low oxygen) cells mature a bit more rapidly. Thus, n(0,t) = F(N(t — d)), (16.33)

where F is some nonlinear production function that is monotone decreasing in its argument. The function F is related to the rate of secretion of erythropoietin in response to the red blood cell population size.

The steady-state solution for this model is easy to determine. We set dn/dt = 0 and find that i n(0)e—jx, x <X, n(x) =] (16.34)

[0, x > X, where n(0) is yet to be determined. If we define N0 to be the total steady-state number of blood cells, then

from which it follows that n(0)

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