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

Leukemia, a type of blood cancer that originates in the bone marrow, is characterized by the uncontrolled growth of abnormal blood cells, which disrupt the normal functioning of blood cells. Chimeric antigen receptor (CAR) T-cell treatment, a form of immunotherapy, utilizes genetically modified T cells to specifically target and eliminate cancer cells. This treatment has shown promising results for leukemia patients who are unresponsive to chemotherapy or other therapies, as well as those who experience relapses.  In this study, we develop a mathematical model of leukemia that incorporates chimeric antigen receptor (CAR) T-cell therapy. The model takes into account the logistic intrinsic growth rate of leukemia cells, which gradually declines over time due to limited resources within the body. There are four compartments in this model: susceptible blood cells, infected blood cells, leukemia cells, and immune cells. We have analyzed the equilibrium points and their local stability, determined the basic reproduction number, and conducted a sensitivity analysis.  Through numerical simulations, we observed that prior to treatment, the number of leukemia cells in the blood escalated rapidly towards endemic conditions. However, after receiving CAR T-cell therapy through external infusion, the leukemia cells either became extinct or took a significant amount of time to reach endemic levels in the blood. Sensitivity analysis revealed that the growth rate of cancer cells (r) and the death rate of immune cells (significantly contribute to the increase in the basic reproduction number (.