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Stability Analysis of a Feedback Model for the Action of theImmune 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: [email protected]
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Abstract

A mathematical model, coupling the dynamics of short-term stem-like cells and matureleukocytes in leukemia with that of the immune system, is investigated. The model isdescribed by a system of seven delay differential equations with seven delays. Threeequilibrium points E0, E1,E2 are highlighted. The stability and the existence of theHopf bifurcation for the equilibrium points are investigated. In the analysis of themodel, the rate of asymmetric division and the rate of symmetric division are veryimportant.

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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