Combination therapy for cancer with IL-27 and anti-PD-1: A simplified mathematical model

Many experiential and clinical trials in cancer treatment show that a combination of immune checkpoint inhibitor with another agent can improve the tumor reduction. Anti Programmed death 1 (Anti-PD-1) is one of these immune checkpoint inhibitors that re-activate immune cells to inhibit tumor growth.  In this work, we consider a combination treatment of anti-PD-1 and Interleukin-27 (IL-27). IL-27 has anti-cancer functions to promote the development of Th1 and CD8$^+$ T cells, but it also upregulates the expression of PD-1 and Programmed death ligand 1 (PD-L1) to inactivate these T cells. Thus, the functions of IL-27 in tumor growth is controversial. Hence, we create a simplified mathematical model to investigate whether IL-27 is pro-cancer or anti-cancer in the combination with anti-PD-1 and to what degree anti-PD-1 improves the efficacy of IL-27. Our synergy analysis for the combination treatment of IL-27 and anti-PD-1 shows that (i) ant-PD-1 can efficiently improve the treatment efficacy of IL-27; and (ii) there exists a monotone increasing function $F_c(G)$ depending on the treatment efficacy of anti-PD-1 $G$ such that IL-27 is an efficient anti-cancer agent when its dose is smaller than $F_c(G)$, whereas IL-27 is a pro-cancer agent when its dose is higher than $F_c(G)$. Our analysis also provides the existence and the local stability of the trivial, non-negative, and positive equilibria of the model. Combining with simulation, we discuss the effect of the IL-27 dosage on the equilibria and find that the T cells and IFN-$\gamma$ could vanish and tumor cells preserve, when the production rate of T cells by IL-27 is low or the dosage of IL-27 is low.