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Modeling and optimal regulation of erythropoiesis subject to benzene intoxication
1.  Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 276958212 
2.  Department of Mathematics and Computer Science, Meredith College, Raleigh, NC 27607, United States 
3.  CIIT Centers for Health Research, Research Triangle Park, NC 27709, United States 
4.  Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695, United States 
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 effects of benzene on hematopoiesis (blood cell production and development). An agestructured 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 differential 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.
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