Mathematical Biosciences and Engineering, 2004, 1(1): 15-48. doi: 10.3934/mbe.2004.1.15.

34K60, 34K35, 65M60, 92C37, 93C20.

Export file:


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


  • Citation Only
  • Citation and Abstract

Modeling and optimal regulation of erythropoiesis subject to benzene intoxication

1. Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695-8212
2. Department of Mathematics and Computer Science, Meredith College, Raleigh, NC 27607
3. CIIT Centers for Health Research, Research Triangle Park, NC 27709
4. Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695

Benzene (C6H6) is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, and industrial processes. Benzene increases the incidence of leukemia in humans when they are exposed to high doses for extended periods; however, leukemia risks in humans subjected to low exposures are uncertain. The exposure-dose- response relationship of benzene in humans is expected to be nonlinear because benzene undergoes a series of metabolic transformations, detoxifying and activating, resulting in various metabolites that exert toxic e ffects on the bone marrow.
    Since benzene is a known human leukemogen, the toxicity of benzene in the bone marrow is of most importance. And because blood cells are produced in the bone marrow, we investigated the eff ects of benzene on hematopoiesis (blood cell production and development). An age-structured model was used to examine the process of erythropoiesis, the development of red blood cells. This investigation proved the existence and uniqueness of the solution of the system of coupled partial and ordinary di fferential equations. In addition, we formulated an optimal control problem for the control of erythropoiesis and performed numerical simulations to compare the performance of the optimal feedback law and another feedback function based on the Hill function.
  Article Metrics

Keywords optimal control.; hematopoiesis; existence and uniqueness; age-structured model

Citation: 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


This article has been cited by

  • 1. 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
  • 2. Pablo Escandell-Montero, Milena Chermisi, José M. Martínez-Martínez, Juan Gómez-Sanchis, Carlo Barbieri, Emilio Soria-Olivas, Flavio Mari, Joan Vila-Francés, Andrea Stopper, Emanuele Gatti, José D. Martín-Guerrero, Optimization of anemia treatment in hemodialysis patients via reinforcement learning, Artificial Intelligence in Medicine, 2014, 62, 1, 47, 10.1016/j.artmed.2014.07.004
  • 3. S. Fischer, P. Kurbatova, N. Bessonov, O. Gandrillon, V. Volpert, F. Crauste, Modeling erythroblastic islands: Using a hybrid model to assess the function of central macrophage, Journal of Theoretical Biology, 2012, 298, 92, 10.1016/j.jtbi.2012.01.002
  • 4. Sibylle Schirm, Christoph Engel, Markus Loeffler, Markus Scholz, Modelling chemotherapy effects on granulopoiesis, BMC Systems Biology, 2014, 8, 1, 10.1186/s12918-014-0138-7
  • 5. O. Hyrien, S. A. Peslak, N. M. Yanev, J. Palis, Stochastic modeling of stress erythropoiesis using a two-type age-dependent branching process with immigration, Journal of Mathematical Biology, 2015, 70, 7, 1485, 10.1007/s00285-014-0803-x
  • 6. 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
  • 7. Fabien Crauste, Laurent Pujo-Menjouet, Stéphane Génieys, Clément Molina, Olivier Gandrillon, Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis, Journal of Theoretical Biology, 2008, 250, 2, 322, 10.1016/j.jtbi.2007.09.041
  • 8. 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
  • 9. Azmy S. Ackleh, Mark L. Delcambre, Karyn L. Sutton, A second-order high-resolution finite difference scheme for a size-structured model for the spread ofMycobacterium marinum, Journal of Biological Dynamics, 2015, 9, sup1, 156, 10.1080/17513758.2014.962998
  • 10. Azmy S. Ackleh, Keng Deng, Kazufumi Ito, Jeremy Thibodeaux, A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate, Mathematical Biosciences, 2006, 204, 1, 21, 10.1016/j.mbs.2006.08.004
  • 11. 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
  • 12. 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
  • 13. 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
  • 14. Cammey C. Manning, Paul M. Schlosser, Hien T. Tran, A Multicompartment Liver-based Pharmacokinetic Model for Benzene and its Metabolites in Mice, Bulletin of Mathematical Biology, 2010, 72, 3, 507, 10.1007/s11538-009-9459-x
  • 15. Jeremy J. Thibodeaux, Michael Hennessey, A Within-Host Model of Dengue Infection with a Non-Constant Monocyte Production Rate, Applied Mathematics, 2016, 07, 18, 2382, 10.4236/am.2016.718187
  • 16. 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
  • 17. Jeremy J. Thibodeaux, Modeling erythropoiesis subject to malaria infection, Mathematical Biosciences, 2010, 225, 1, 59, 10.1016/j.mbs.2010.02.001
  • 18. Doris H. Fuertinger, Franz Kappel, Stephan Thijssen, Nathan W. Levin, Peter Kotanko, A model of erythropoiesis in adults with sufficient iron availability, Journal of Mathematical Biology, 2013, 66, 6, 1209, 10.1007/s00285-012-0530-0
  • 19. Sibylle Schirm, Christoph Engel, Markus Loeffler, Markus Scholz, Pranela Rameshwar, A Biomathematical Model of Human Erythropoiesis under Erythropoietin and Chemotherapy Administration, PLoS ONE, 2013, 8, 6, e65630, 10.1371/journal.pone.0065630
  • 20. Fabien Crauste, Ivan Demin, Olivier Gandrillon, Vitaly Volpert, Mathematical study of feedback control roles and relevance in stress erythropoiesis, Journal of Theoretical Biology, 2010, 263, 3, 303, 10.1016/j.jtbi.2009.12.026
  • 21. Jeremy J. Thibodeaux, Daniel Nuñez, Andres Rivera, A generalized within-host model of dengue infection with a non-constant monocyte production rate, Journal of Biological Dynamics, 2020, 14, 1, 143, 10.1080/17513758.2020.1733678

Reader Comments

your name: *   your email: *  

Copyright Info: 2004, H. T. Banks, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved