Asynchronous exponential growth in an age structured population of proliferating and quiescent cells

Blood Cell Dynamics: Half of a Century of Modelling

“…New fields were investigated also like chaos of hematopoietic cell population with Crabb et al [93]. Note that this theme started to be trendy during this period for hematopoiesis modeling since it was also studied by Webb and collaborators from an analytical point of view: through instability of solutions and hypercyclicity [104], [117], [118], [119], [120]. Some review papers about models of hematopoietic cell replication and control were published to set up a state of the art after three decades of work on this field [42], [193], [44], [152].…”

“…For the models and theory initiated in the previous decades, it was interesting to notice that asymptotic exponential growth applied to blood problems was not trendy any more, and to the best of our knowledge no work was developed besides [123]. Quite popular in the 1980's, this property may come back on the foreground in the next decades for new hematological equations.…”

Analysis of a System Describing Proliferative-Quiescent Cell Dynamics

“…Systems describing the dynamics of proliferative and quiescent cells are commonly used as computational models, for instance for tumor growth and hematopoiesis [4,10,14,15,16,23]. The typical dynamical system, introduced in the papers of Gyllenberg and Webb [13], describes the populations n P (t) ≥ 0 (proliferative cells) and n Q (t) ≥ 0 (quiescent cells) with a control by the total population n(t), as…”

Oscillations in a molecular structured cell population model

“…Since then, many researchers have contributed to this field (see for instance [13], [4] , [5], [2]). Cell structured population models with proliferating and quiescent compartments have also been extensively studied (see for instance [12], [17], [11]). …”