A. Kaddar, H. Talibi Alaoui (2010)
Mathematical Modelling of Natural Phenomena
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This paper is devoted to the study of global existence of periodic solutions of a delayed tumor-immune competition model. Also some numerical simulations are given to illustrate the theoretical results
Buckingham, David J., Callahan, Paul B. (1998)
Experimental Mathematics
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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...
Panetta, John Carl (1998)
Journal of Theoretical Medicine
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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...
Mahiéddine Kouche, Bedr'eddine Ainseba (2010)
International Journal of Applied Mathematics and Computer Science
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In this paper we derive a model describing the dynamics of HIV-1 infection in tissue culture where the infection spreads directly from infected cells to healthy cells trough cell-to-cell contact. We assume that the infection rate between healthy and infected cells is a saturating function of cell concentration. Our analysis shows that if the basic reproduction number does not exceed unity then infected cells are cleared and the disease dies out. Otherwise, the infection is persistent...
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...