Mathematical modeling of B-cell chronic lymphocytic leukemia and immune systems with therapy

Abstract

A quantitative understanding of the dynamics of the immune system to treatment is important in planning treatment strategies, such as timing, dosing, and predicting the response to a certain treatment. In this context, mathematical modeling of the relationship between disease-causing cells and the immune system, along with treatment, is one of the effective methods. In this study, we establish a nonlinear dynamical system that models the interaction between B-cell chronic lymphocytic leukemia and the immune system with a chemo-drug. We examined behaviour of the solution of the system around equilibrium points via phase-space analysis. Local stability analysis is performed on the nonlinear system, and stability conditions are also derived in the Lyapunov sense. Finally, numerical results are obtained with respect to the cases, tumor size, parameter change, and drug addition.