The development of vaccines geared towards the generation of a CD8 T cell immunity may provide protection from diseases caused by intra-cellular pathogens with high mutational rates that escape humoral surveillance. However, the development and monitoring of vaccines in pre-clinical models is a long process and tools, such as mathematical models, that could predict the generation of memory CD8 T cells from early events of the response, would help saving time and money and would improve ethical issues. We have previously developed a minimal mathematical model that captures the dynamics of a CD8 T cell response described in the literature. Here, we will describe an extension of this model that allows the description of CD8 T cell responses to infections with a live pathogen. This model can fit three series of experimental data of the total CD8 T cell dynamics in response to influenza and vaccinia viruses as well as Listeria monocytogenes infections. Systematic analysis of the parameter space identified common and specific features of the three responses and demonstrated the robustness and predictive capacity of the model.