Study of the behaviour of proliferating cells in leukemia modelled by a system of delay differential equations

Anca Veronica Ion

doi:10.1515/auom-2015-0048

.blurhash-client-img { display: none !important; }

Study of the behaviour of proliferating cells in leukemia modelled by a system of delay differential equations

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 23 (2015): Issue 3 (November 2015)

By: Anca Veronica Ion

Open Access

|Apr 2017

Abstract

For the model of periodic chronic myelogenous leukemia considered by Pujo-Menjouet, Mackey et al., model consisting of two delay differential equations, the equation for the density of so-called “resting cells” was studied from numerical and qualitative point of view in several works. In this paper we focus on the equation for the density of proliferating cells and study it from a qualitative point of view.

References

[1] Adelina Georgescu, I. Oprea, Bifurcation theory from application view-point, Tipografia Univ. Timișoara, 1994, (Monografii Matematice 51).
Search in Google Scholar Back to article
[2] A. Halanay, Qualitative theory of differential equations, Editura Academiei Republicii Populare Române, 1963. (in Romanian)
Search in Google Scholar Back to article
[3] A. V. Ion, New results concerning the stability of equilibria of a delay differential equation modeling leukemia, Proceedings of The 12th Symposium of Mathematics and its Applications, Timișoara, November 5-7, 2009, 375-380; arXiv:1001.4658.
Search in Google Scholar Back to article
[4] A. V. Ion, R. M. Georgescu, Stability of equilibrium and periodic solutions of a delay equation modeling leukemia, Works of the Middle Volga Mathematical Society, 11(2009); arXiv:1001.5354.
Search in Google Scholar Back to article
[5] A. V. Ion, R.M. Georgescu, Bautin bifurcation in a delay differential equation modeling leukemia, Nonlinear Analysis, 82(2013), 142-157.10.1016/j.na.2013.01.009
Search in Google Scholar Back to article
[6] Y. A. Kuznetsov, Elements of applied bifurcation theory, Applied Mathematical Sciences, 112, Springer, New York, 1998.
Search in Google Scholar Back to article
[7] L. Pujo-Menjouet, M. C. Mackey, Contribution to the study of periodic chronic myelogenous leukemia, C. R. Biologies, 327(2004), 235-244.10.1016/j.crvi.2003.05.00415127894
Search in Google Scholar Back to article
[8] L. Pujo-Menjouet, S. Bernard, M. C. Mackey, Long period oscillations in a G0 model of hematopoietic stem cells, SIAM J. Applied Dynamical Systems, 2, 4(2005), 312-332.10.1137/030600473
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/auom-2015-0048 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 65 - 81

Submitted on: Nov 1, 2014

Accepted on: Jan 1, 2015

Published on: Apr 22, 2017

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

leukemia model,

delay differential equations,

qualitative analysis,

Related subjects:

© 2017 Anca Veronica Ion, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 23 (2015): Issue 3 (November 2015)