A study on fractional-order mathematical and parameter analysis for CAR T-cell therapy for leukemia using homotopy perturbation method

Abstract

Leukemia is a malignant blood cancer that originates in the bone marrow is typified by the uncontrolled proliferation of aberrant blood cells. Globally, it is one of the main causes of health issues. In this study, we present a fractional-order four compartmental mathematical model (MM) of leukemia, which includes susceptible blood cells S₁(t), infected blood cells I₁(t), cancer cells C₁(t), and immune blood cells W₁(t), and we analyze the dynamics of transmission of the disease. We use the homotopy perturbation method (HPM) to develop analytical solutions and classical fourth-order Runge-Kutta (RK4) approach to obtain numerical solutions for the mathematical model (MM) of leukemia. Moreover, the concerned solutions which have been found using the methods are compared. For the fractional parameter of α = 0.25, the result shows that the fractional order (FO) model gives better accuracy and stability compared to the conventional integer-order model. For that reason, we emphasize the significance of FO modeling in understanding the spread of leukemia.