2008, 5(4): 601-616. doi: 10.3934/mbe.2008.5.601

Parameter estimation in a structured erythropoiesis model


Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010, United States


Department of Mathematics and Statistics, University of Central Oklahoma, Edmond, Oklahoma 73034, United States

Received  December 2007 Revised  May 2008 Published  October 2008

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. Mathematical Biosciences & Engineering, 2008, 5 (4) : 601-616. doi: 10.3934/mbe.2008.5.601

Qihua Huang, Hao Wang. A toxin-mediated size-structured population model: Finite difference approximation and well-posedness. Mathematical Biosciences & Engineering, 2016, 13 (4) : 697-722. doi: 10.3934/mbe.2016015


Azmy S. Ackleh, H.T. Banks, Keng Deng, Shuhua Hu. Parameter Estimation in a Coupled System of Nonlinear Size-Structured Populations. Mathematical Biosciences & Engineering, 2005, 2 (2) : 289-315. doi: 10.3934/mbe.2005.2.289


Azmy S. Ackleh, Vinodh K. Chellamuthu, Kazufumi Ito. Finite difference approximations for measure-valued solutions of a hierarchically size-structured population model. Mathematical Biosciences & Engineering, 2015, 12 (2) : 233-258. doi: 10.3934/mbe.2015.12.233


Alex Capaldi, Samuel Behrend, Benjamin Berman, Jason Smith, Justin Wright, Alun L. Lloyd. Parameter estimation and uncertainty quantification for an epidemic model. Mathematical Biosciences & Engineering, 2012, 9 (3) : 553-576. doi: 10.3934/mbe.2012.9.553


Blaise Faugeras, Olivier Maury. An advection-diffusion-reaction size-structured fish population dynamics model combined with a statistical parameter estimation procedure: Application to the Indian Ocean skipjack tuna fishery. Mathematical Biosciences & Engineering, 2005, 2 (4) : 719-741. doi: 10.3934/mbe.2005.2.719


Gianni Gilioli, Sara Pasquali, Fabrizio Ruggeri. Nonlinear functional response parameter estimation in a stochastic predator-prey model. Mathematical Biosciences & Engineering, 2012, 9 (1) : 75-96. doi: 10.3934/mbe.2012.9.75


Mou-Hsiung Chang, Tao Pang, Moustapha Pemy. Finite difference approximation for stochastic optimal stopping problems with delays. Journal of Industrial and Management Optimization, 2008, 4 (2) : 227-246. doi: 10.3934/jimo.2008.4.227


Giovanna Citti, Maria Manfredini, Alessandro Sarti. Finite difference approximation of the Mumford and Shah functional in a contact manifold of the Heisenberg space. Communications on Pure and Applied Analysis, 2010, 9 (4) : 905-927. doi: 10.3934/cpaa.2010.9.905


Sebastian Springer, Heikki Haario, Vladimir Shemyakin, Leonid Kalachev, Denis Shchepakin. Robust parameter estimation of chaotic systems. Inverse Problems and Imaging, 2019, 13 (6) : 1189-1212. doi: 10.3934/ipi.2019053


Gonzalo Galiano, Julián Velasco. Finite element approximation of a population spatial adaptation model. Mathematical Biosciences & Engineering, 2013, 10 (3) : 637-647. doi: 10.3934/mbe.2013.10.637


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. Mathematical Biosciences & Engineering, 2014, 11 (4) : 679-721. doi: 10.3934/mbe.2014.11.679


Mostafa Adimy, Abdennasser Chekroun, Tarik-Mohamed Touaoula. Age-structured and delay differential-difference model of hematopoietic stem cell dynamics. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 2765-2791. doi: 10.3934/dcdsb.2015.20.2765


Simon Hubmer, Andreas Neubauer, Ronny Ramlau, Henning U. Voss. On the parameter estimation problem of magnetic resonance advection imaging. Inverse Problems and Imaging, 2018, 12 (1) : 175-204. doi: 10.3934/ipi.2018007


Robert Azencott, Yutheeka Gadhyan. Accurate parameter estimation for coupled stochastic dynamics. Conference Publications, 2009, 2009 (Special) : 44-53. doi: 10.3934/proc.2009.2009.44


Claire david@lmm.jussieu.fr David, Pierre Sagaut. Theoretical optimization of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 286-293. doi: 10.3934/proc.2007.2007.286


Chongyang Liu, Meijia Han, Zhaohua Gong, Kok Lay Teo. Robust parameter estimation for constrained time-delay systems with inexact measurements. Journal of Industrial and Management Optimization, 2021, 17 (1) : 317-337. doi: 10.3934/jimo.2019113


Krzysztof Fujarewicz, Krzysztof Łakomiec. Parameter estimation of systems with delays via structural sensitivity analysis. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2521-2533. doi: 10.3934/dcdsb.2014.19.2521


Dominique Chapelle, Philippe Moireau, Patrick Le Tallec. Robust filtering for joint state-parameter estimation in distributed mechanical systems. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 65-84. doi: 10.3934/dcds.2009.23.65


Andrea Arnold, Daniela Calvetti, Erkki Somersalo. Vectorized and parallel particle filter SMC parameter estimation for stiff ODEs. Conference Publications, 2015, 2015 (special) : 75-84. doi: 10.3934/proc.2015.0075


Alessandro Corbetta, Adrian Muntean, Kiamars Vafayi. Parameter estimation of social forces in pedestrian dynamics models via a probabilistic method. Mathematical Biosciences & Engineering, 2015, 12 (2) : 337-356. doi: 10.3934/mbe.2015.12.337

2018 Impact Factor: 1.313


  • PDF downloads (42)
  • HTML views (0)
  • Cited by (11)

Other articles
by authors

[Back to Top]