Application of the multi-step differential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells

Human T-cell Lymphotropic Virus I (HTLV-I) infection of $CD4^{+}$ T-Cells is one of the causes of health problems and continues to be one of the significant health challenges. In this article, a multi-step differential transform method is implemented to give approximate solutions of fractional modle of HTLV-I infection of $CD4^{+}$ T-cells. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method in the case of intger-order derivatives. The suggested method is efficient as the Runge-Kutta method. Some plots are presented to show the reliability and simplicity of the method.