Modeling the effect of adoptive T cell therapy for the treatment of leukemia

Abstract

Leukemia is a malignant cancer of the blood. It is the most common type of cancer in children. In this paper, a mathematical model of leukemia in terms of ordinary differential equations has been developed. We propose a model to study the spread of leukemia by considering the effect of adoptive T cell therapy. The disease dynamics are given by a system of ordinary nonlinear differential equations that describe the interaction among susceptible blood cells, infected blood cells, cancer cells, and immune cells. The model is analyzed by using the stability theory of nonlinear differential equations and numerical simulations. A major goal of this work is to determine the spread of leukemia after applying the adoptive T cell therapy. We have observed that the system is stable locally and globally if stimulation rate or antigenicity rate of immune cells is greater than a threshold value dependent on the density of immune cells in the blood. We have also observed that the external reinfusion of immune cells by adoptive T cell therapy reduces the concentration of cancer cells and infected cells in the blood, which implies that immune cells kill cancer cells after being stimulated in the body.