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Stability Analysis of a Feedback Model for the Action of the Immune System in Leukemia

Published online by Cambridge University Press:  07 February 2014

S. Balea ,
A. Halanay ,
D. Jardan ,
M. Neamţu  and
C. A. Safta
S. Balea
Affiliation:
“POLITEHNICA” University of Bucharest Department of Mathematics and Informatics Splaiul Independentei 313 RO-060042 Bucharest, Romania
A. Halanay
Affiliation:
“POLITEHNICA” University of Bucharest Department of Mathematics and Informatics Splaiul Independentei 313 RO-060042 Bucharest, Romania
D. Jardan
Affiliation:
“POLITEHNICA” University of Bucharest Department of Mathematics and Informatics Splaiul Independentei 313 RO-060042 Bucharest, Romania
M. Neamţu*
Affiliation:
“POLITEHNICA” University of Bucharest Department of Mathematics and Informatics Splaiul Independentei 313 RO-060042 Bucharest, Romania West University of Timisoara, Department of Economics and Modelling 300115 Pestalozzi Str. 16, Timisoara, Romania
C. A. Safta
Affiliation:
“POLITEHNICA” University of Bucharest Department of Mathematics and Informatics Splaiul Independentei 313 RO-060042 Bucharest, Romania
*
⋆ Corresponding author. E-mail: mihaela.neamtu@feaa.uvt.ro
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Abstract

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.

Keywords

immune systemleukemiadelay differential equationsstabilityHopf bifurcationlimit cycle
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 1: Issue dedicated to Michael Mackey , 2014 , pp. 108 - 132
Copyright
© EDP Sciences, 2014

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