## 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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##### Cite this paper as:

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

## About this paper

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##### Online ISSN

**2073-8994**

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