| Issue |
Math. Model. Nat. Phenom.
Volume 9, Number 1, 2014
Issue dedicated to Michael Mackey
|
|
|---|---|---|
| Page(s) | 108 - 132 | |
| DOI | https://doi.org/10.1051/mmnp/20149108 | |
| Published online | 07 February 2014 | |
Stability Analysis of a Feedback Model for the Action of the Immune System in Leukemia
1 “POLITEHNICA” University of Bucharest
Department of Mathematics and Informatics Splaiul Independentei 313
RO-060042
Bucharest,
Romania
2 West University of Timisoara,
Department of Economics and Modelling 300115 Pestalozzi Str. 16,
Timisoara,
Romania
⋆
Corresponding author. E-mail: mihaela.neamtu@feaa.uvt.ro
A mathematical model, coupling the dynamics of short-term stem-like cells and mature leukocytes in leukemia with that of the immune system, is investigated. The model is described by a system of seven delay differential equations with seven delays. Three equilibrium points E0, E1, E2 are highlighted. The stability and the existence of the Hopf bifurcation for the equilibrium points are investigated. In the analysis of the model, the rate of asymmetric division and the rate of symmetric division are very important.
Mathematics Subject Classification: 34K20 / 37G15 / 92D25
Key words: immune system / leukemia / delay differential equations / stability / Hopf bifurcation / limit cycle
© EDP Sciences, 2014
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