Analysis of unstable behavior in a mathematical model for erythropoiesis

Susana Serna; Jasmine A. Nirody; Miklós Z. Rácz

doi:https://doi.org/10.1007/s00285-012-0524-y

Analysis of unstable behavior in a mathematical model for erythropoiesis

Susana Serna, Jasmine A. Nirody, Miklós Z. Rácz

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

We consider an age-structured model that describes the regulation of erythropoiesis through the negative feedback loop between erythropoietin and hemoglobin. This model is reduced to a system of two ordinary differential equations with two constant delays for which we show existence of a unique steady state. We determine all instances at which this steady state loses stability via a Hopf bifurcation through a theoretical bifurcation analysis establishing analytical expressions for the scenarios in which they arise. We show examples of supercritical Hopf bifurcations for parameter values estimated according to physiological values for humans found in the literature and present numerical simulations in agreement with the theoretical analysis. We provide a strategy for parameter estimation to match empirical measurements and predict dynamics in experimental settings, and compare existing data on hemoglobin oscillation in rabbits with predictions of our model. © 2012 Springer-Verlag.

Original language	English
Pages (from-to)	595-625
Journal	Journal of Mathematical Biology
Volume	66
Issue number	3
DOIs	https://doi.org/10.1007/s00285-012-0524-y
Publication status	Published - 1 Jan 2013

Keywords

Age-structured model
Erythropoiesis
Hopf bifurcation
Multiple delay differential equations

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title = "Analysis of unstable behavior in a mathematical model for erythropoiesis",

abstract = "We consider an age-structured model that describes the regulation of erythropoiesis through the negative feedback loop between erythropoietin and hemoglobin. This model is reduced to a system of two ordinary differential equations with two constant delays for which we show existence of a unique steady state. We determine all instances at which this steady state loses stability via a Hopf bifurcation through a theoretical bifurcation analysis establishing analytical expressions for the scenarios in which they arise. We show examples of supercritical Hopf bifurcations for parameter values estimated according to physiological values for humans found in the literature and present numerical simulations in agreement with the theoretical analysis. We provide a strategy for parameter estimation to match empirical measurements and predict dynamics in experimental settings, and compare existing data on hemoglobin oscillation in rabbits with predictions of our model. {\textcopyright} 2012 Springer-Verlag.",

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AU - Nirody, Jasmine A.

AU - Rácz, Miklós Z.

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N2 - We consider an age-structured model that describes the regulation of erythropoiesis through the negative feedback loop between erythropoietin and hemoglobin. This model is reduced to a system of two ordinary differential equations with two constant delays for which we show existence of a unique steady state. We determine all instances at which this steady state loses stability via a Hopf bifurcation through a theoretical bifurcation analysis establishing analytical expressions for the scenarios in which they arise. We show examples of supercritical Hopf bifurcations for parameter values estimated according to physiological values for humans found in the literature and present numerical simulations in agreement with the theoretical analysis. We provide a strategy for parameter estimation to match empirical measurements and predict dynamics in experimental settings, and compare existing data on hemoglobin oscillation in rabbits with predictions of our model. © 2012 Springer-Verlag.

AB - We consider an age-structured model that describes the regulation of erythropoiesis through the negative feedback loop between erythropoietin and hemoglobin. This model is reduced to a system of two ordinary differential equations with two constant delays for which we show existence of a unique steady state. We determine all instances at which this steady state loses stability via a Hopf bifurcation through a theoretical bifurcation analysis establishing analytical expressions for the scenarios in which they arise. We show examples of supercritical Hopf bifurcations for parameter values estimated according to physiological values for humans found in the literature and present numerical simulations in agreement with the theoretical analysis. We provide a strategy for parameter estimation to match empirical measurements and predict dynamics in experimental settings, and compare existing data on hemoglobin oscillation in rabbits with predictions of our model. © 2012 Springer-Verlag.

KW - Age-structured model

KW - Erythropoiesis

KW - Hopf bifurcation

KW - Multiple delay differential equations

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