A TUMOR-IMMUNE MODEL WITH MIXED IMMUNOTHERAPY AND CHEMOTHERAPY: QUALITATIVE ANALYSIS AND OPTIMAL CONTROL

We develop a mathematical model of tumor-immune interactions, including six populations (tumor cells, CD8(+)T cells, natural killer (NK) cells, dendritic cells, helper T cells, cytokine interleukin-12 (IL-12)) and three potential treatments (chemotherapy, Tumor-infiltrating lymphocyte (TIL) therapy and IL-12 therapy). We characterize the dynamics of our model without treatment through stability and sensitivity analysis, which provides a broad understanding of the long-term qualitative behavior. To find the best combination of the chemo-immunotherapy regimens to eliminate tumors, we formulate an optimal control problem with path constraints of total drug dose and solve it numerically with the optimal control software Pyomo. We also simulate the scenarios of traditional treatment protocols as a comparison and find that our optimal treatment strategies have a better therapeutic effect. In addition, numerical simulation results show that IL-12 therapy is a good adjunctive therapy and has a high potential for inhibiting a large tumor in combination with other therapy. In most cases, combination therapy is more effective than a single treatment.