Modeling the Dynamics of Chronic Myelogenous Leukemia Through Fractional-Calculus

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.