Philip Korman (2016)
Annales Polonici Mathematici
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We prove the existence and uniqueness of a positive periodic solution for a model describing the dynamics of cell volume flux, introduced by Julio A. Hernández [Bull. Math. Biol. 69 (2007), 1631-1648]. We also show that the periodic solution is a global attractor. Our results confirm the conjectures made in an interesting recent book of P. J. Torres [Atlantis Press, 2015].
A. Halanay (2012)
Mathematical Modelling of Natural Phenomena
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Existence and stability of periodic solutions are studied for a system of delay differential equations with two delays, with periodic coefficients. It models the evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding function leads to the proof of the existence of a strictly positive periodic solution by a theorem...
J. Clairambault, S. Gaubert, Th. Lepoutre (2009)
Mathematical Modelling of Natural Phenomena
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We study the growth rate of a cell population that follows an age-structured PDE with time-periodic coefficients. Our motivation comes from the comparison between experimental tumor growth curves in mice endowed with intact or disrupted circadian clocks, known to exert their influence on the cell division cycle. We compare the growth rate of the model controlled by a time-periodic control on its coefficients with the growth rate of stationary models of the same nature, but with averaged...
J. Ligęza (1977)
Annales Polonici Mathematici
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Stanisław Sędziwy (1972)
Annales Polonici Mathematici
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Papini, Duccio, Zanolin, Fabio (2004)
Fixed Point Theory and Applications [electronic only]
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G. J. Butler (1974)
Annales Polonici Mathematici
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G. J. Butler, H. I. Freedman (1979)
Annales Polonici Mathematici
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N. Bessonov, L. Pujo-Menjouet, V. Volpert (2010)
Mathematical Modelling of Natural Phenomena
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In this work, we introduce a new software created to study hematopoiesis at the cell population level with the individually based approach. It can be used as an interface between theoretical works on population dynamics and experimental observations. We show that this software can be useful to study some features of normal hematopoiesis as well as some blood diseases such as myelogenous leukemia. It is also possible to simulate cell communication and the formation of cell colonies in...