Homotopy Perturbation Approach to Fractional-Order CAR T-Cell Therapy with Cytokines in Leukemia

Abstract

Leukemia is a type of blood cancer marked by the irregular proliferation of cells that originate in the bone marrow, representing a major global health concern. This research introduces a fractional-order (FO) five-compartment mathematical model for leukemia, which includes susceptible blood cells s₁(t), infected blood cells i₁(t), cancer cells c₁(t), immune blood cells w₁(t), and cytokine cells c₂(t). The homotopy perturbation method (HPM) is employed to derive analytical solutions, whereas the fourth-order Runge-Kutta (RK4) method is utilized to calculate numerical solutions for the CAR-T cell therapy model. This model is structured to investigate the dynamics of the disease, and a comparative analysis is performed between the analytical and numerical outcomes. For the fractional parameter a = 0.45, The results demonstrate that the FO model provides higher accuracy and stability in contrast to the conventional integer-order model. Consequently, FO modeling is essential for comprehending leukemia dynamics and highlights the critical necessity for global access to this form of immunotherapy.