Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous Leukemia

Cell Modelling of Hematopoiesis

“…The most recent models in blood diseases in the literature are the so-called maturity-agetime structured models consisting of a system of partial differential equations describing instability of the cell population facing aplastic anemia [3,4,13,14]. Some other deterministic models using either systems of differential equations or age structured systems deal with cyclical neutropenia [5,6,16,17], thrombocytopenia [25,26], or chronic myelogenous leukemia [1,2,10,22,23,24]. It is important here to notice that most of the continuous models deal with density only while our approach in the paper is to consider a population of individual cells.…”

Blood Cell Dynamics: Half of a Century of Modelling

“…This latter became a great hit during the years 2000's. CML was then studied in a great variety of ways, from general models trying to describe the regulating process of oscillating populations through many different feedback (mostly cause by stimulating growth factors) in differential or structured differential equations, with or without delays [25], [26], [134], [230], [201], [83], [84], [82], [112], [85], [231], [148], [215], [216], [240], [245], [138], [150], [3], [24], [113].…”

On the Dynamics of an Impulsive Model of Hematopoiesis

“…Taking into account that all stem cells do not require the same time in cell cycle to divide, Adimy et al [4] studied models similar to the one proposed by Mackey [19], but with a time delay distributed according to a density with compact support. They highlighted the role of a destabilization of the cell cycle duration in the appearance of oscillating solutions with long periods (see [22]). …”