Loading [Contrib]/a11y/accessibility-menu.js
Search Advanced

Mathematical Biosciences and Engineering

2008, Volume 5, Issue 4: 601-616. doi: 10.3934/mbe.2008.5.601
Previous Article Next Article

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
  • Received: 01 December 2007 Accepted: 29 June 2018 Published: 01 October 2008

  • MSC : Primary: 92C37, 65M06

  • 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.

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

    Related Papers:

    [1] H. T. Banks, Cammey E. Cole, Paul M. Schlosser, Hien T. Tran . Modeling and optimal regulation of erythropoiesis subject to benzene intoxication. Mathematical Biosciences and Engineering, 2004, 1(1): 15-48. doi: 10.3934/mbe.2004.1.15
    [2] Azmy S. Ackleh, Vinodh K. Chellamuthu, Kazufumi Ito . Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model. Mathematical Biosciences and Engineering, 2015, 12(2): 233-258. doi: 10.3934/mbe.2015.12.233
    [3] Azmy S. Ackleh, H.T. Banks, Keng Deng, Shuhua Hu . Parameter Estimation in a Coupled System of Nonlinear Size-Structured Populations. Mathematical Biosciences and Engineering, 2005, 2(2): 289-315. doi: 10.3934/mbe.2005.2.289
    [4] Yuganthi R. Liyanage, Nora Heitzman-Breen, Necibe Tuncer, Stanca M. Ciupe . Identifiability investigation of within-host models of acute virus infection. Mathematical Biosciences and Engineering, 2024, 21(10): 7394-7420. doi: 10.3934/mbe.2024325
    [5] Lernik Asserian, Susan E. Luczak, I. G. Rosen . Computation of nonparametric, mixed effects, maximum likelihood, biosensor data based-estimators for the distributions of random parameters in an abstract parabolic model for the transdermal transport of alcohol. Mathematical Biosciences and Engineering, 2023, 20(11): 20345-20377. doi: 10.3934/mbe.2023900
    [6] Scott R. Pope, Laura M. Ellwein, Cheryl L. Zapata, Vera Novak, C. T. Kelley, Mette S. Olufsen . Estimation and identification of parameters in a lumped cerebrovascular model. Mathematical Biosciences and Engineering, 2009, 6(1): 93-115. doi: 10.3934/mbe.2009.6.93
    [7] Alex Capaldi, Samuel Behrend, Benjamin Berman, Jason Smith, Justin Wright, Alun L. Lloyd . Parameter estimation and uncertainty quantification for an epidemic model. Mathematical Biosciences and Engineering, 2012, 9(3): 553-576. doi: 10.3934/mbe.2012.9.553
    [8] Kimberlyn Roosa, Ruiyan Luo, Gerardo Chowell . Comparative assessment of parameter estimation methods in the presence of overdispersion: a simulation study. Mathematical Biosciences and Engineering, 2019, 16(5): 4299-4313. doi: 10.3934/mbe.2019214
    [9] Maria Pia Saccomani, Karl Thomaseth . Calculating all multiple parameter solutions of ODE models to avoid biological misinterpretations. Mathematical Biosciences and Engineering, 2019, 16(6): 6438-6453. doi: 10.3934/mbe.2019322
    [10] Keenan Hawekotte, Susan E. Luczak, I. G. Rosen . Deconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a Bayesian approach. Mathematical Biosciences and Engineering, 2021, 18(5): 6739-6770. doi: 10.3934/mbe.2021335
  • 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.


  • This article has been cited by:

    1. L. Pujo-Menjouet, V. Volpert, Blood Cell Dynamics: Half of a Century of Modelling, 2016, 11, 0973-5348, 92, 10.1051/mmnp/201611106
    2. Manuel Tetschke, Patrick Lilienthal, Torben Pottgiesser, Thomas Fischer, Enrico Schalk, Sebastian Sager, Mathematical Modeling of RBC Count Dynamics after Blood Loss, 2018, 6, 2227-9717, 157, 10.3390/pr6090157
    3. 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, 2018, 13, 1932-6203, e0195918, 10.1371/journal.pone.0195918
    4. Azmy S. 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, 2014, 11, 1551-0018, 679, 10.3934/mbe.2014.11.679
    5. Azmy S. Ackleh, Jeremy J. Thibodeaux, A second-order finite difference approximation for a mathematical model of erythropoiesis, 2013, 0749159X, n/a, 10.1002/num.21778
    6. O. Angulo, F. Crauste, J.C. López-Marcos, Numerical integration of an erythropoiesis model with explicit growth factor dynamics, 2018, 330, 03770427, 770, 10.1016/j.cam.2017.01.033
    7. 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, 2013, 245, 00255564, 2, 10.1016/j.mbs.2013.03.007
    8. Jeremy J. Thibodeaux, Timothy P. Schlittenhardt, Optimal Treatment Strategies for Malaria Infection, 2011, 73, 0092-8240, 2791, 10.1007/s11538-011-9650-8
    9. 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, 2013, 110, 00063592, 3024, 10.1002/bit.24968
    10. O. Angulo, O. Gandrillon, F. Crauste, Investigating the role of the experimental protocol in phenylhydrazine-induced anemia on mice recovery, 2018, 437, 00225193, 286, 10.1016/j.jtbi.2017.10.031
    11. Jeremy J. Thibodeaux, Modeling erythropoiesis subject to malaria infection, 2010, 225, 00255564, 59, 10.1016/j.mbs.2010.02.001
  • Reader Comments
  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(2833) PDF downloads(492) Cited by(11)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog