The surface protein B7-H1, also called PD-L1 and CD274, is found on carcinomas of the lung, ovary, colon, and melanomas but not on most normal tissues. B7-H1 has been experimentally determined to be an antiapoptotic receptor on cancer cells, where B7-H1-positive cancer cells have been shown to be immune resistant, and in vitro experiments and mouse models have shown that B7-H1-negative tumor cells are significantly more susceptible to being repressed by the immune system. We derive a new mathematical model for studying the interaction between cytotoxic T cells and tumor cells as affected by B7-H1. By integrating experimental data into the model, we isolate the parameters that control the dynamics and obtain insights on the mechanisms that control apoptosis.