International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 32, Pages 2011-2026
doi:10.1155/S0161171203211431

A semilinear transport equation with delays

Janet Dyson,1 Rosanna Villella-Bressan,2 and Glenn F. Webb3

 1Mansfield College, Oxford OX1 3TF, UK
2Dipartimento di Matematica Pura ed Applicata, Universitá di Padova, Padova, Italy
3Department of Mathematics, Vanderbilt University, Nashville 37235, TN, USA
Received 26 November 2002

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.