PERIODICALLY PULSED IMMUNOTHERAPY IN A MATHEMATICAL MODEL OF TUMOR-IMMUNE INTERACTION

Abstract

Immunotherapy is one of the most recent approaches in cancer therapy. In this paper, a mathematical model of tumor-immune interaction with periodically pulsed immunotherapy, which is described by impulsive differential equations, is considered. The ODE system is turned into a discrete-time dynamical system for bifurcation analysis. A mathematical analysis is performed to determine the minimum dosage for successful treatment. An adaptive grid method is then developed to identify the fixed points and their bifurcations. The effects of continuous and pulsed treatment strategies are compared. The interindividual variability is studied by one-parameter and two-parameter bifurcation diagrams. Increasing the strength of the immune response improves the outcome of the treatment if the immune response is weak. However, it becomes a drawback when the strength of the immune response increases over a certain threshold. Multiple attractors exist so that a treatment may result in a tumor-free state, a large tumor, or a middle-sized tumor depending on initial conditions. It is believed that the numerical method proposed in this paper can be applied to a class of mathematical models of periodically pulsed drug therapies.