Mathematical model for IL-2-based cancer immunotherapy

Abstract

A basic mathematical model for IL-2-based cancer immunotherapy is proposed and studied. Our analysis shows that the outcome of therapy is mainly determined by three parameters, the relative death rate of CD$4^{+}$ T cells, the relative death rate of CD$8^{+}$ T cells, and the dose of IL-2 treatment. Minimal equilibrium tumor size can be reached with a large dose of IL-2 in the case that CD$4^{+}$ T cells die out. However, in cases where CD$4^{+}$ and CD$8^{+}$ T cells persist, the final tumor size is independent of the IL-2 dose and is given by the relative death rate of CD$4^{+}$ T cells. Two groups of in silico clinical trials show some short-term behaviors of IL-2 treatment. IL-2 administration can slow the proliferation of CD$4^{+}$ T cells, while high doses for a short period of time over several days transiently increase the population of CD$8^{+}$ T cells during treatment before it recedes to its equilibrium. IL-2 administration for a short period of time over many days suppresses the tumor population for a longer time before approaching its steady-state levels. This implies that intermittent administration of IL-2 may be a good strategy for controlling tumor size.