Abstract
In this paper, two control problems for a symmetric model of cell dynamics related to leukemia are considered. The first one, in connection with classical chemotherapy, is that the evolution of the disease under treatment should follow a prescribed trajectory assuming that the drug works by increasing the cell death rates of both malignant and normal cells. In the case of the second control problem, as for targeted therapies, the drug is assumed to work by decreasing the multiplication rate of leukemic cells only, and the control objective is that the disease state reaches a desired endpoint. The solvability of the two problems as well as their stability are proved by using a general method of analysis. Some numerical simulations are included to illustrate the theoretical results and prove their applicability. The results can possibly be used to design therapeutic scenarios such that an expected clinical evolution can be achieved.
Authors
Ioan Ştefan Haplea
Department of Internal Medicine, Iuliu Hatieganu University of Medicine and Pharmacy, 400012 Cluj-Napoca, Romania; haplea.ioan.stefan@gmail.com
Lorand Gabriel Parajdi
Department of Mathematics, West Virginia University, USA
Department of Mathematics, Babeş–Bolyai University, Cluj-Napoca, Romania
Radu Precup
Institute of Advanced Studies in Science and Technology STAR-UBB, Babeş-Bolyai University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
Keywords
control problem; dynamic system; leukemia
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I.Ş. Haplea, L.G. Parajdi, R. Precup, On the controllability of a system modeling cell dynamics related to leukemia, Symmetry, 13 (2021) no. 10, doi: 10.3390/sym13101867
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