A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia

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dc.creatorAdimy, Mostafa
dc.creatorCrauste, Fabien
dc.creatorRuan, Shigui
dc.date2009-04-16
dc.date.accessioned2026-07-07T13:05:02Z
dc.date.available2026-07-07T13:05:02Z
dc.descriptionThis paper is devoted to the analysis of a mathematical model of blood cells production in the bone marrow (hematopoiesis). The model is a system of two age-structured partial differential equations. Integrating these equations over the age, we obtain a system of two nonlinear differential equations with distributed time delay corresponding to the cell cycle duration. This system describes the evolution of the total cell populations. By constructing a Lyapunov functional, it is shown that the trivial equilibrium is globally asymptotically stable if it is the only equilibrium. It is also shown that the nontrivial equilibrium, the most biologically meaningful one, can become unstable via a Hopf bifurcation. Numerical simulations are carried out to illustrate the analytical results. The study maybe helpful in understanding the connection between the relatively short cell cycle durations and the relatively long periods of peripheral cell oscillations in some periodic hematological diseases.
dc.identifierhttps://arxiv.org/abs/0904.2493
dc.identifierhttp://arxiv.org/abs/0904.2493
dc.identifierSIAM Journal on Applied Mathematics 65, 4 (2005) 1328-1352
dc.identifierdoi:10.1137/040604698
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227371
dc.subjectAnalysis of PDEs
dc.subjectCell Behavior
dc.subjectTissues and Organs
dc.titleA mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia
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