RESUMO
We construct a multi-stage cell lineage model for cell division, apoptosis and movement. Cells are assumed to secrete and respond to negative feedback molecules which act as a control on the stem cell divisions (including self-renewal, asymmetrical cell division (ACD) and differentiation). The densities of cells and molecules are described by coupled reaction-diffusion partial differential equations, and the plane wavefront propagation speeds can be obtained analytically and verified numerically. It is found that with ACD the population and propagation of stem cells can be promoted but the negative regulation on self-renewal and differentiation will work slowly. Regulatory inhibition on differentiation will inversely increase stem cells but not affect the population and wave propagation of the cell lineage. While negative regulation on self-renewal and ACD will decrease the population of stem cells and slow down the propagation, and even drive stem cells to extinction. Moreover we find that inhibition on self-renewal has a strength advantage while inhibition on ACD has a range advantage to kill stem cells. Possible relations to model cancer development and therapy are also discussed.