A study on fractional-order mathematical analysis for inspecting the spread of the leukemia virus

Abstract

Leukemia is the name for a blood cancer that develops in the bone marrow. Leukemia is a global public health issue caused by the uncontrolled growth of immature white blood cells in the bloodstream. In this study, we consider a fractional-order five-compartment mathematical model (MM) of leukemia, which includes susceptible blood cells$S_1\left(t\right)$, infected blood cells $I_1\left(t\right)$, cancer cells $C_1\left(t\right)$, immune blood cells $W_1\left(t\right)$, cytokine cells $C_2\left(t\right)$, and we analyze the dynamics of transmission of the disease. We developed a model to examine the spread of the leukemia virus and analyze the effects of adoptive T-cell therapy. This study presents a model of the well-known leukemia virus utilizing Caputo fractional order (CFO) and Beta derivatives. In this, the extended system characterizing the virus spread is addressed using two analytical methods: the Laplace perturbation method (LPM) and the Homotopy decomposition method (HDM). Iterative schemes were employed to obtain specific solutions of the extended system, and numerical simulations were conducted based on selected theoretical parameters. Moreover, the concerned analytical solutions that have been found using the methods are compared. The corresponding plots against various orders of the differentiations are plotted using specific values for the model’s parameters. We emphasize the significance of fractional-order (FO) modeling in understanding the spread of leukemia and highlight the critical need for global access to this immunotherapy.