A fractional‐order model for chronic lymphocytic leukemia and immune system interactions

Abstract

In this study, a mathematical, fractional-order model was developed for B cell chronic lymphocytic leukemia, with immune system, and then analyzed. Interactions between B leukemia cells, natural killer cells, cytotoxic T cells, and T-helper cells are considered to be incorporated into a system consisting of four fractional differential equations. For estimation of the parameters, clinical data of six patients were used. By numerical solution of the system, the interactions between the leukemia cell population and the immune system cell populations for values of ∈ (0, 1) at different times were explained. By determining points of equilibrium and stability of the system were met. Bifurcation analysis showed that use of the fractional-order model, figure out unpredictable behaviors of the system such as saddle-node, bistability and hysteresis phenomenon occurred in the system by changing the values of some of the parameters, it was predictable. KEYWORDS bifurcation, chronic lymphocytic leukemia, mathematical model of fractional-order, stability analysis MSC CLASSIFICATION 92XX; 92Bxx 1 INTRODUCTION 1.1 Chronic lymphocytic leukemia background B cell chronic lymphocytic leukemia (B-CLL) is a progressive and malignant disease of the hematopoietic organs of the body. The disease is caused by the impaired proliferation and development of white blood cell and its precursors in the blood, bone marrow, spleen, and lymph nodes. The excess production of blood cell is abnormal in bone marrow leukemia. These cells differ from blood cells and do not function appropriately. Consequently, the production of normal white blood cells stops and eliminates the individual's ability to cope with disease. Leukemia cancer cells also have a negative effect on the production of other types of blood cells that are produced by the bone marrow, including red blood cells, which transport oxygen to the tissues of the body, and blood platelets, which prevent blood clotting. Therefore, in a variety of leukemia, weak immunity, anemia, and impaired blood clotting may occur. 1,2 Given the fact that there is no proper theory of cancer, scientific advances in the treatment of this disease are almost confined to trial and error, and clinical tests are used to diagnose drug efficacy.

Mathematical Model of Leukemia Treatment with Chimeric Antigen Receptor (CAR) T Cell Therapy

“…(Moore & Li, 2004), (Dimitriu, 2019), (Valle et al, 2021), and (Karg et al, 2022), proposed and analyzed the dynamical model of chronic myelogenous leukemia. In addition, (Guzev et al, 2022), (Rodrigues et al, 2019), and (Fadaei et al, 2021) formulate and analyse a mathematical model of chronic lymphocytic leukemia with a treatment such as chemotherapy or chemoimmunotherapy.…”

FPGA Implementation of Parameter-Switching Scheme to Stabilize Chaos in Fractional Spherical Systems and Usage in Secure Image Transmission

“…energy systems [4], and quantum systems [5]; in biology, modeling in cell biology [6], cancer biology [7], and computational biology [8,9]; in engineering, dynamics and control [10,11], fluid mechanics and aerodynamics [12,13], and telecommunication [14,15]. These are some areas where fractional calculus is applied.…”