| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
|
|
|---|---|---|
| Article Number | 68 | |
| Number of page(s) | 23 | |
| DOI | https://doi.org/10.1051/mmnp/2020038 | |
| Published online | 03 December 2020 | |
Mathematical analysis and global dynamics for a time-delayed Chronic Myeloid Leukemia model with treatment
1
Biomathematics Laboratory, Univ. Sidi Bel-Abbes,
P.B. 89,
22000, Algeria.
2
Laboratoire d’Analyse Nonlinéaire et Mathématiques Appliquées, Univ. Tlemcen, Algeria.
* Corresponding author: mhelal_abbes@yahoo.fr
Received:
10
March
2020
Accepted:
22
October
2020
In this paper, we investigate a time-delayed model describing the dynamics of the hematopoietic stem cell population with treatment. First, we give some property results of the solutions. Second, we analyze the asymptotic behavior of the model, and study the local asymptotic stability of each equilibrium: trivial and positive ones. Next, a necessary and sufficient condition is given for the trivial steady state to be globally asymptotically stable. Moreover, the uniform persistence is obtained in the case of instability. Finally, we prove that this system can exhibits a periodic solutions around the positive equilibrium through a Hopf bifurcation.
Mathematics Subject Classification: 34D20 / 34D23 / 34K05 / 92C37
Key words: Delay differential system / Lyapunov function / global stability / stability switch / Hopf bifurcation / cell dynamics
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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