Induction of antitumor immunity by vaccination is one of the major current immunotherapy strategies. We present a mathematical model of the competition between immune cells and mammary carcinogenesis under the effect of Triplex vaccine. The model describes both humoral and cell-mediated immune responses against cancer cells. The control of the cancer cells growth occurs through the application of the pulse vaccination. Here we determine the relationship between the strength of the vaccine and the time required to eradicate cancer cells, and we present some simulations to illustrate our theoretical results, namely, the total cancer cells depletion, which is influenced by competition occurs among the immune and cancer cells.