Journal
JOURNAL OF BIOLOGICAL DYNAMICS
Volume 6, Issue -, Pages 2-18Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17513758.2011.558214
Keywords
cell production systems; stem cell population dynamics; stability analysis; reproduction number
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Funding
- Spanish Ministry of Science and Innovation (MICINN) [MTM2010 - 18318]
- ERC
- German Research Council (DFG)
- [SFB 873]
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We study two- and three-compartment models of a hierarchical cell production system with cell division regulated by the level of mature cells. We investigate the structure of equilibria with respect to parameters as well as local stability properties for the equilibria. To interpret the results we adapt the concept of reproduction numbers, which is well known in ecology, to stem cell population dynamics. In the two-compartment model, the positive equilibrium is stable wherever it exists. In the three-compartment model, we find that the intermediate stage of differentiation is responsible for the emergence of an instability region in the parameter plane. Moreover, we prove that this region shrinks as the mortality rate for mature cells increases and discuss this result.
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