A Mathematical Analysis of the Interactions between Immunogenic Tumor Cells and Cytotoxic T Lymphocytes

Recent developments of biotechnology have enabled us to use immunotherapy against certain kinds of tumors in patients. However, it is reasonable to doubt if the immunotherapy can completely aid the rejection of tumors that have escaped from the immune system. In this paper, we propose a new mathematical model of tumor immunity by tumor‐specific cytotoxic T lymphocytes (CTLs), since tumor‐specific CTLs play an important role in tumor immunity. Using this model, we have mathematically investigated the interactions between immunogenic tumor cells (TCs) and tumor‐specific CTLs and evaluated the availability of immunotherapies for tumors. The findings herein demonstrate that three kinds of dynamics of tumor immunity exist: i.e. (1) TCs continue to proliferate with CTLs; (2) TCs are rejected by CTLs; and (3) TCs equilibrate with CTLs, but with little possibility of the equilibrium. The findings also demonstrate that a sufficient increase in CTLs by immunotherapy can aid the rejection of TCs, but an insufficient increase in CTLs by immunotherapy causes only a transient regression of TCs. Clinically the findings mean that increasing tumor‐specific CTLs, e.g., by vaccination or adoptive transfer of tumor‐specific CTLs expanded ex vivo, can theoretically aid the rejection of TCs.