Abstract
An analysis is provided for a model of the blood production system based on a cell population structured by a continuous variable corresponding to the maturity of individual cells. Cell maturity is viewed as an indicator of increasing morphological development, ranging from the most primitive stem cells to the most mature differentiated cells. The analysis distinguishes two fundamental behaviors based on the nature of the initial state of the system: the first is a normal production of cells, when the initial state contains a sufficient supply of the least mature cells; the second is an abnormal production, when the initial state is deficient in the population of the least mature cells.
Highlights
We investigate a singular transport equation which arises as a model of the blood production system
In the model we study here, which was developed by Rey and Mackey in [10], the blood production system is viewed as a population of cells with individual cells distinguished by a maturity variable x
By successive divisions cell lines progress through increasingly mature cell types, which enter into the blood circulation
Summary
We investigate a singular transport equation which arises as a model of the blood production system. For the existence and uniqueness of solutions, we require continuity and, in certain cases, differentiability conditions on f . If τ = 0 and f is only continuous, solutions may not always exist, as we showed in [2] for the particular cases g(x) = x and f (x) = μx(1 − x).
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