Parameter estimation in a structured erythropoiesis model

Azmy S. Ackleh; Jeremy J. Thibodeaux; Azmy S. Ackleh; Jeremy J. Thibodeaux

doi:10.3934/mbe.2008.5.601

Mathematical Biosciences and Engineering

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

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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.
- erythropoiesis,
- structured model,
- finite difference approximation,
- parameter estimation
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

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Abstract

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.
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