MODELING THE DYNAMICS OF CHRONIC MYELOGENOUS LEUKEMIA THROUGH FRACTIONAL-CALCULUS

Tao-Qian Tang, Rashid Jan, Ziad Ur Rehman, Zahir Shah, Narcisa Vrinceanu and Mihaela Racheriu
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Tao-Qian Tang: International Intercollegiate Ph.D. Program, National Tsing Hua University, Hsinchu 30013, Taiwan2Department of Internal Medicine, E-DA Hospital, Kaohsiung 82445, Taiwan3School of Medicine, College of Medicine, I-Shou University, Kaohsiung 82445, Taiwan4Department of Family and Community Medicine, E-DA Hospital, Kaohsiung 82445, Taiwan5Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan
Rashid Jan: Department of Mathematics, University of Swabi, Swabi 23430, Khyber Pakhtunkhwa, Pakistan
Ziad Ur Rehman: Department of Mathematics, University of Swabi, Swabi 23430, Khyber Pakhtunkhwa, Pakistan
Zahir Shah: Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan
Narcisa Vrinceanu: Department of Industrial Machines and Equipment, Faculty of Engineering, “Lucian Blaga†University of Sibiu, 10 Victoriei Boulevard, Sibiu 550024, Romania
Mihaela Racheriu: Faculty of Medicine, “Lucian Blaga†University of Sibiu, Strada 2A Lucian Blaga, Sibiu 550169, Romania10County Clinical Emergency Hospital, 2-4 Corneliu Coposu Str., Sibiu 550245, Romania

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-16

Abstract: Although the therapy of chronic myelogenous leukemia (CML) has progressed because of imatinib (IM) and other tyrosine kinase inhibitors (TKIs), the majority of patients still do not recover. To better regulate the remaining leukemic cell population, TKI combo therapy may be improved with a deeper understanding of the underlying mechanisms. We employed a mathematical system which incorporated the intricate phenomena of immune system to CML. We use a fractional derivative framework in this work to understand the dynamics of CML. Additionally, in our work, we concentrate on the qualitative characterization and dynamical behavior of CML interactions. For the proposed model, we examine the singularity and existence using fixed point theorems by Banach and Schaefer. We provide the necessary criteria for our suggested fractional model’s Ulam–Hyers stability. The influence of the factors on the dynamics of CML is highlighted by closely examining the solution paths by using a numerical scheme. To be more precise, we emphasized how the suggested system’s dynamic and chaotic behavior varied depending on the fractional order and other system factors. Policymakers are advised to consider the most crucial elements of CML dynamics. In order to inform policymakers and health authorities about the systems essential for control and treatment, it is crucial to investigate the dynamic characteristics of CML disease.

Keywords: Chronic Myelogenous Leukemia (CML); Fractional Dynamics; Stability Results; Immune System; Numerical Analysis; Dynamical Behavior (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402629

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