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A mathematical approach to cell dynamics before and after allogeneic bone marrow transplantation. (English) Zbl 1402.92155

Summary: We shortly survey our recent contributions for a basic theoretical-mathematical understanding of cell dynamics in acute leukemia, before and after allogeneic bone marrow transplantation. Inspired by the approach of D. Dingli and F. Michor [“Successful therapy must eradicate cancer stem cells”, Stem Cells 24, No. 12, 2603–2610 (2006; doi:10.1634/stemcells.2006-0136)], our theoretical models are given in terms of two- and three-dimensional ordinary differential systems whose parameters take into account essential biological properties, processes and interactions, and are involved in the characterization of normal or abnormal hematopoietic status, in the description of asymptotically stable steady-states and their basins of attraction and of therapeutic pre- and post-transplant strategies.

MSC:

92C37 Cell biology
92C50 Medical applications (general)
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