Journal of Mathematical Biology

, Volume 66, Issue 3, pp 595–625 | Cite as

Analysis of unstable behavior in a mathematical model for erythropoiesis

  • Susana SernaEmail author
  • Jasmine A. Nirody
  • Miklós Z. Rácz


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.


Age-structured model Multiple delay differential equations Hopf bifurcation Erythropoiesis 

Mathematics Subject Classification

35Q92 37N25 92C50 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Susana Serna
    • 1
    Email author
  • Jasmine A. Nirody
    • 2
  • Miklós Z. Rácz
    • 3
  1. 1.Departament de MatematiquesUniversitat Autonoma de BarcelonaBellaterra, BarcelonaSpain
  2. 2.Department of Radiology and Biomedical ImagingUniversity of CaliforniaSan FranciscoUSA
  3. 3.Department of StatisticsUniversity of CaliforniaBerkeleyUSA

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