Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Parameter estimation in a structured erythropoiesis model

1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010
2. Department of Mathematics and Statistics, University of Central Oklahoma, Edmond, Oklahoma 73034

We develop a numerical method for estimating parameters in a structured erythropoiesis model consisting of a nonlinear system of partial differential equations. Convergence theory for the computed parameters is provided. Numerical results for estimating the growth rate of precursor cells as a function of the erythropoietin concentration and the decay rate of erythropoietin as a function of the total number of precursor cells from computationally generated data are provided. Standard errors for such parameters are also given.
  Figure/Table
  Supplementary
  Article Metrics

Keywords erythropoiesis; structured model; finite difference approximation; parameter estimation

Citation: Azmy S. Ackleh, Jeremy J. Thibodeaux. Parameter estimation in a structured erythropoiesis model. Mathematical Biosciences and Engineering, 2008, 5(4): 601-616. doi: 10.3934/mbe.2008.5.601

 

This article has been cited by

  • 1. L. Pujo-Menjouet, V. Volpert, Blood Cell Dynamics: Half of a Century of Modelling, Mathematical Modelling of Natural Phenomena, 2016, 11, 1, 92, 10.1051/mmnp/201611106
  • 2. Doris H. Fuertinger, Franz Kappel, Hanjie Zhang, Stephan Thijssen, Peter Kotanko, Kostas Pantopoulos, Prediction of hemoglobin levels in individual hemodialysis patients by means of a mathematical model of erythropoiesis, PLOS ONE, 2018, 13, 4, e0195918, 10.1371/journal.pone.0195918
  • 3. Azmy Ackleh, Mark L. Delcambre, Karyn L. Sutton, Don G. Ennis, A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme, Mathematical Biosciences and Engineering, 2014, 11, 4, 679, 10.3934/mbe.2014.11.679
  • 4. Azmy S. Ackleh, Jeremy J. Thibodeaux, A second-order finite difference approximation for a mathematical model of erythropoiesis, Numerical Methods for Partial Differential Equations, 2013, n/a, 10.1002/num.21778
  • 5. O. Angulo, F. Crauste, J.C. López-Marcos, Numerical integration of an erythropoiesis model with explicit growth factor dynamics, Journal of Computational and Applied Mathematics, 2018, 330, 770, 10.1016/j.cam.2017.01.033
  • 6. Azmy S. Ackleh, Baoling Ma, Jeremy J. Thibodeaux, A second-order high resolution finite difference scheme for a structured erythropoiesis model subject to malaria infection, Mathematical Biosciences, 2013, 245, 1, 2, 10.1016/j.mbs.2013.03.007
  • 7. Jeremy J. Thibodeaux, Timothy P. Schlittenhardt, Optimal Treatment Strategies for Malaria Infection, Bulletin of Mathematical Biology, 2011, 73, 11, 2791, 10.1007/s11538-011-9650-8
  • 8. Joshua A. Selekman, Amritava Das, Nicholas J. Grundl, Sean P. Palecek, Improving efficiency of human pluripotent stem cell differentiation platforms using an integrated experimental and computational approach, Biotechnology and Bioengineering, 2013, 110, 11, 3024, 10.1002/bit.24968
  • 9. O. Angulo, O. Gandrillon, F. Crauste, Investigating the role of the experimental protocol in phenylhydrazine-induced anemia on mice recovery, Journal of Theoretical Biology, 2018, 437, 286, 10.1016/j.jtbi.2017.10.031
  • 10. Jeremy J. Thibodeaux, Modeling erythropoiesis subject to malaria infection, Mathematical Biosciences, 2010, 225, 1, 59, 10.1016/j.mbs.2010.02.001
  • 11. Manuel Tetschke, Patrick Lilienthal, Torben Pottgiesser, Thomas Fischer, Enrico Schalk, Sebastian Sager, Mathematical Modeling of RBC Count Dynamics after Blood Loss, Processes, 2018, 6, 9, 157, 10.3390/pr6090157

Reader Comments

your name: *   your email: *  

Copyright Info: 2008, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved