A Control Delay Differential Equations Model of Evolution of Normal and Leukemic Cell Populations Under Treatment

Abstract : The dynamics and evolution of leukemia is determined by the interactions between normal and leukemic cells populations at every phase of the development of hematopoietic cells. For both types of cell populations, two subpopulations are considered, namely the stem-like cell population (i.e. with unlimited self-renew ability) and a more mature, differentiated one, possessing only the capability to undergo limited reproduction. Treatment effects are included in the model as functions of time and a cost functional is considered. The optimal control is obtained using a discretization scheme. Numerical results are discussed in relation to the medical interpretation.
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Chapitre d'ouvrage
Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. System Modeling and Optimization : 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9–13, 2013, Revised Selected Papers, AICT-443, Springer Berlin Heidelberg, pp.257-266, 2014, IFIP Advances in Information and Communication Technology, 978-3-662-45503-6. 〈10.1007/978-3-662-45504-3_25〉
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I. Rădulescu, Doina Cândea, Andrei Halanay. A Control Delay Differential Equations Model of Evolution of Normal and Leukemic Cell Populations Under Treatment. Christian Pötzsche; Clemens Heuberger; Barbara Kaltenbacher; Franz Rendl. System Modeling and Optimization : 26th IFIP TC 7 Conference, CSMO 2013, Klagenfurt, Austria, September 9–13, 2013, Revised Selected Papers, AICT-443, Springer Berlin Heidelberg, pp.257-266, 2014, IFIP Advances in Information and Communication Technology, 978-3-662-45503-6. 〈10.1007/978-3-662-45504-3_25〉. 〈hal-01286684〉

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